Ellen Kuhl

Global food systems must deliver nutritious, sustainable foods while sharply reducing environmental impact. Yet, food innovation remains slow, empirical and fragmented. Artificial intelligence (AI) offers a transformative path to link molecular composition to functional performance, connect chemical structure to sensory outcomes and accelerate cross-disciplinary innovation across the production pipeline. While it is broadly applicable to food systems, we focus on sustainable proteins-plant-based, fermentation-derived and cultivated-as a high-impact test bed for AI-driven closed-loop design. We review the applications, opportunities and challenges of AI for food as an emerging discipline that integrates ingredient design, formulation development, fermentation and production, texture analysis, sensory science, manufacturing and recipe generation. We identify four priorities: advancing scientific machine learning with embedded domain priors, treating food as a programmable biomaterial, building self-driving laboratories for automated discovery and developing deep reasoning models that integrate nutrition and sustainability. Integrating AI responsibly into the food innovation cycle can accelerate the transition to sustainable food systems and establish a predictive, design-driven science of food for human and planetary health.

Food choices shape both human and planetary health; yet, designing foods that are delicious, nutritious, and sustainable remains challenging. Here we show that generative artificial intelligence can learn the structure of the human palate directly from large-scale, human-generated recipe data to create novel foods within a structured design space. Using burgers as a model system, the generative AI rediscovers the classic Big Mac without explicit supervision and generates novel burgers optimized for deliciousness, sustainability, or nutrition. Compared to the Big Mac, its delicious burgers score the same or better in overall liking, flavor, and texture in a blinded sensory evaluation conducted in a restaurant setting with 101 participants; its mushroom burger achieves an environmental impact score more than an order of magnitude lower; and its bean burger attains nearly twice the nutritional score. Together, these results establish generative AI as a quantitative framework for learning human taste and navigating complex trade-offs in principled food design.

Abstract Texture is one of the major barriers to acceptance of sustainable protein products, yet the relationship between instrumental texture and consumer perception remains poorly understood. Here we combined consumer sensory evaluation and texture profile analysis to identify the factors that drive burger acceptance across blended, animal-based, and plant-based formulations. A total of 472 diners evaluated beef-mushroom ( n = 171), turkey ( n = 100), bean ( n = 100), and pea ( n = 101) burgers served in Stanford University dining halls, while texture profile analysis quantified physical texture ( n = 10 per product). The beef-mushroom burger achieved the highest ratings for meatiness (77.0/100), tastiness (69.4/100), and moistness (61.8/100), and 78% of consumers rated its moistness as just-about-right. Although the pea burger exhibited mechanical properties similar to the beef-mushroom burger, including indistinguishable cohesiveness values (0.53 vs. 0.53), it received substantially lower ratings for meatiness (56.1 vs. 77.0), indicating that mechanical similarity alone does not ensure consumer acceptance. Across products, moistness emerged as the primary sensory limitation, with 58% of turkey consumers and 46% of bean consumers reporting insufficient moisture. Cohesiveness showed the strongest association with perceived meatiness ( r = 0.82). These findings demonstrate that successful burger reformulation requires more than mechanical matching; products must reproduce the moisture, flavor, and eating experience associated with meat. Blended burgers may represent the most practical near-term strategy for reducing meat consumption without compromising eating quality.

Global food production must reduce environmental impact while meeting rising demand for dietary protein. Plant-based meats aim to preserve the sensory and cultural role of animal meat while lowering greenhouse gas emissions, land use, and health risks. Advances in protein structure and flavor chemistry have improved product quality, yet consumers continue to prioritize taste and texture over sustainability, and systematic large-scale consumer surveys are scarce. It remains unclear how plant-based products rank against animal benchmarks and which product attributes most strongly influence overall liking. Here we show, in a large-scale blinded in-person sensory evaluation across 14 product categories, 2684 consumers, more than 11,000 product evaluations and 800,000 data points, that plant-based products still trail animal benchmarks at the category average level but approach parity in selected formats. Plant-based unbreaded chicken filets, chicken nuggets, and burgers achieved mean overall liking scores of 5.1, 4.9, and 5.2, differing from the animal benchmarks by only Δ = 0.1, 0.2, and 0.3 points on a seven-point scale. For unbreaded chicken filets and burgers, 48% and 47% of the participants rated the plant-based product the same as or better than the animal benchmark. Categories with higher sensory parity captured 5-14% market share compared with less than 1% for low-parity categories. Penalty analysis identified savoriness, aftertaste, juiciness, and tenderness as the strongest determinants of liking. These findings show that sensory parity is technically achievable but not yet consistent across product types. By publicly sharing all the sensory, preference, and market-linked data, we establish an open benchmark for alternative protein performance to democratize research and accelerate principled data-driven innovation.

Can we learn the physics of matter in motion directly from images and video--and trust it? Answering this question requires integrating experiments, physics-based simulation, and data across traditionally separate disciplines. Much of this knowledge is visual and temporal rather than textual: images and videos encode structure, dynamics, and causality that equations alone cannot fully capture. Recent generative models produce compelling visual content, yet they rely on observational data and often lack physical validity. Here we show that generative video models gain scientific value when they couple visual data with experiments and high-fidelity simulations. Using deformation mechanics as a testbed, we study three systems of increasing complexity--rubber compression, can crushing, and cardiac motion--and identify regimes in which visual learning succeeds, fails, and requires mechanistic supervision. When physics manifests in visible kinematics, generative models recover measurable quantities such as surface strain; when internal state variables dominate, visual plausibility no longer ensures physical admissibility. We propose that this convergence defines a new frontier, the Generative Sciences of Matter and Motion, which unifies Simulogenics, Physiogenics, and Materiogenics. These physics-grounded foundation models can turn visual generation into a scientific instrument for inference, prediction, and design of matter in motion.

Fungal protein materials exhibit inherently anisotropic microstructures formed by networks of hyphae, which suggest a natural pathway to replicate the fibrous texture of animal meat. We probe whether this structural anisotropy translates into macroscopic mechanical and sensory anisotropy. Using orthogonal tension, compression, and shear experiments on three fungi-based materials, we identify distinct symmetry classes that range from strongly anisotropic to effectively isotropic behavior. Automated model discovery reveals that fiber-dependent invariants emerge only when mechanically relevant, and enables direct identification of material symmetry from data. These results demonstrate that microstructural anisotropy does not universally imply anisotropic mechanics or perception and establish a data-driven framework to infer symmetry in complex soft materials.

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and–unlike conventional convex formulations–satisfies the dissipation inequality without requiring convexity. Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To circumvent the use of exponential-map time integration during training–which often leads to numerical instabilities–we employ recurrent Liquid Neural Networks as an auxiliary architecture. During inference, however, the exponential-map update is reinstated to ensure admissibility of the inelastic variables. The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via Zenodo.org .

Material Fingerprinting is an emerging approach for the rapid discovery of mechanical material models directly from experimental data. By interpreting a material’s response in standardized experiments as its fingerprint, Material Fingerprinting employs pattern recognition to match experimental data against a precomputed database, enabling real-time model discovery. This strategy is both fast and robust, as it avoids solving potentially non-convex optimization problems. Unlike traditional calibration methods, Material Fingerprinting simultaneously selects the most suitable material model and identifies its parameters. Since the fingerprint database is fully controllable, the method guarantees interpretable and physically meaningful models. In previous work, we showed the feasibility of this concept for experiments with homogeneous or heterogeneous deformation fields using synthetically generated data. Here we present the first experimental validation of Material Fingerprinting. We carefully design a fingerprint database for uniaxial tension/compression, equibiaxial tension as well as pure and simple shear experiments. Once computed in an offline phase, this database can be reused for rapid model discovery across diverse experimental datasets. We demonstrate that this single database enables the robust and efficient discovery of hyperelastic strain energy functions to accurately characterize the isotropic mechanical responses of rubber, hydrogel, and brain tissue in less than one second on a standard personal computer. To make this approach openly accessible for rapid material model discovery across laboratories, we release the database and the implementation of Material Fingerprinting as a pip-installable Python package alongside this publication.

Understanding the physiological condition of the vascular system is critical to explain, treat, and manage vascular disease. Numerous experimental and computational studies characterize the mechanical behavior of arterial tissue under controlled laboratory conditions. However, translating this knowledge into physiologically realistic conditions remains challenging. Key difficulties include selecting suitable and relevant test methods, minimizing uncertainty, and ensuring robust model validation. Here, we present a novel integrative approach to translate laboratory experiments on arterial samples into clinically relevant pressure-diameter behavior. We perform controlled planar-biaxial tests on carotid arteries under three stretch ratios and generate axial and circumferential stress-stretch data to calibrate a fiber-reinforced soft tissue model. Using an analytical thick-walled cylindrical model, we predict subject-specific pressure-diameter behavior, informed by arterial prestretches from ring opening experiments. We systematically compare predictions against extension-inflation experiments on tubes from the same artery by applying controlled pairs of axial stretch and inner pressure, while recording outer diameter. We quantify prediction error in absolute and relative stretch regimes and evaluate the importance of the load-free reference dimensions. Results show how planar-biaxial tests probe different stretch regimes compared to extension-inflation deformations, leading to extrapolation of model predictions. We demonstrate how the constitutive material parameters can be fitted to different biomechanical loading conditions, and we assess the sensitivity of the simulations to axial stretch and circumferential prestretch. Only when those key model parameters are accurately captured and their uncertainty propagated, planar-biaxial stress-stretch data can reliably predict arterial pressure-diameter behavior.

This repository accompanies the work “A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains”. It contains the complete implementation of the neural network–based constitutive modeling framework presented in the paper. The provided code includes neural network models for anisotropic and inelastic materials, their training scripts, and finite element simulations using the learned constitutive laws. The directory NN_Ani_Inelastic_Just_Code/ is organized into three main modules (the directory NN_Ani_Inelastic/ includes all results such as network weights, ParaView files, and training data ): 01_NN/ – Neural Network constitutive models.This folder contains the core implementation of the inelastic constitutive artificial neural networks (iCANNs) used for isotropic and anisotropic materials. ConstiNNscripts/: Definitions of neural constitutive models, recurrent architectures (RNN_iCANN), cell formulations, and exponential map integrators. NNscripts/: Supporting network architectures such as ICNNs, monotonic networks, and helper utilities for constraint application. CONTIscripts/: Continuum mechanics helper functions, including invariants, deviatoric projections, and generating functions. TRAINscripts/: Training routines for different constitutive settings (e.g., isotropic vs. one-fiber anisotropy, liquid-EM models, exponential map integrators). train_PWTEH_.py* and eval_PWTEH_.py*: Top-level training and evaluation scripts for plane strain problems. RESULTS/ and DATA/: Folders prepared for storing output data and model checkpoints. 02_FEM/ – Finite element simulations using the trained neural constitutive models.This module provides the finite element solver and scripts to run benchmark problems such as the Cook’s membrane with and without holes. FEMscripts/: Core FEM routines, including mesh handling, shape functions (Q1 elements), time integration, and neural-network–based material models. 00_meshes/: Input mesh files (.inp) for the test cases (e.g., Cook with hole, plate with two holes, PWTEH geometry). main_CookWH_.py*: Simulation scripts for isotropic and anisotropic neural materials as well as purely mechanical reference cases. 01_results/: Folder intended for storing FEM results. 03_RNN/ – Temporal constitutive models using recurrent architectures.This folder includes implementations and training scripts for recurrent neural networks capturing history-dependent (inelastic) material behavior. RNN.py and LiNN.py: Core recurrent formulations for incremental constitutive updates. main_RNN_ani.py and main_LiNN_ani.py: Training and evaluation scripts for anisotropic materials. main_RNN_iso.py and main_LiNN_iso.py: Isotropic counterparts. run_training.sh: Example shell script for automated model training. The requirements.txt file lists all necessary Python dependencies for reproducing the results. This dataset provides the complete codebase for training, evaluating, and coupling neural constitutive models with a finite element framework. It enables reproduction of the results shown in the paper for both isotropic and anisotropic inelastic materials, including path-dependent and rate-dependent responses modeled through RNN-based architectures. The provided scripts and model definitions can be directly extended for new material systems or benchmark problems in computational mechanics.

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven framework that simultaneously discovers appropriate invariants and constitutive models for isotropic incompressible hyperelastic materials. Our approach identifies both the most suitable invariants in a class of generalized invariants and the corresponding strain energy function directly from experimental observations. Unlike previous methods that rely on fixed invariant choices or sequential fitting procedures, our method integrates the discovery process into a single neural network architecture. By looking at a continuous family of possible invariants, the model can flexibly adapt to different material behaviors. We demonstrate the effectiveness of this approach using popular benchmark datasets for rubber and brain tissue. For rubber, the method recovers a stretchdominated formulation consistent with classical models. For brain tissue, it identifies a formulation sensitive to small stretches, capturing the nonlinear shear response characteristic of soft biological matter. Compared to traditional and neural-network-based models, our framework provides improved predictive accuracy and interpretability across a wide range of deformation states. This unified strategy offers a robust tool for automated and physically meaningful model discovery in hyperelasticity.

We present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture’s design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX , is publicly accessible at https://doi.org/10.5281/zenodo.14894687 .

AutoEncoder Architectures This repository accompanies the preprint“Autoencoder-based non-intrusive model order reduction in continuum mechanics”. It provides the AutoEncoder architectures, regression models, and reference simulation data used in the numerical experiments of the paper. The content is organized by case study, and each folder contains both reference FEM data(PureFEM) and the corresponding AutoEncoder-based surrogate models (AE_and_FFN). Folder Structure 01_Unit_Cell/ 01_PureFEM/ – Reference FEM simulations of the heterogeneous composite unit cell. 02_AE_and_FFN/ – Implementation and training of the AutoEncoder (unsupervised) combined with a Feed-Forward Network for latent space regression. 02_Plate_with_Elliptic_Hole/ 01_PureFEM/ – FEM simulations of a plate with a parametrized elliptic hole (geometry variation with parameters xi, eta). 02_AE_and_FFN/ – Complete AutoEncoder and regression setup. AEscripts/ – AutoEncoder architecture, training steps, and loss functions. FFNtoLSscripts/ – Feed-forward regression models mapping input parameters to the latent space. 01_results/ – Example runs including training histories (lossAE_history.txt, lossFFNtoLS_history.txt) and comparisons of reference and predicted meshes (mesh_reference.vtu, mesh_prediction.vtu). 03_Thermo_imperfection/ 01_PureFEM/ – Thermo-mechanical FEM simulations with geometric imperfections. 02_AE_and_FFN/ – Extended AutoEncoder setup for multi-field problems (temperature + displacement). Includes separate training histories for thermal and mechanical quantities (lossFFNtoLS_Temp_history.txt, lossFFNtoLS_disp_history.txt). 04_Thermo/ 01_PureFEM/ – Thermo-mechanical FEM simulations of a plate for varying parameters (xi, eta). Contains .vtu output files documenting transient solution states. Contents PureFEM folders – Reference finite element solutions (ground truth data). AE_and_FFN folders – AutoEncoder and regression architectures, including training scripts and configuration files. 01_results folders – Training and evaluation results: Loss histories for AutoEncoder and regression networks. Prediction vs. reference mesh files (.vtu, .inp). Timing information (training_evaluation_times.txt). Purpose This dataset provides the complete implementation and results required to reproduce the numerical experiments presented in the paper. It covers: Unit cell with heterogeneous microstructure – Displacement and force prediction. Plate with elliptic hole – Parametric geometry variation and anisotropic elasticity. Thermo-mechanical problem with imperfections – Multi-field AutoEncoder with coupled displacement and temperature. Thermo-mechanical plate – Transient analysis and surrogate reconstruction. The provided files are intended to help users quickly identify the relevant scripts and data for each study and to facilitate reproduction, extension, or adaptation of the presented AutoEncoder-based non-intrusive model order reduction framework.

Computational modeling has become an integral tool for understanding the interaction between structural organization and functional behavior in a wide range of biological tissues, including the human myocardium. Traditional constitutive models, and recent models generated by automated model discovery, are often based on the simplifying assumption of perfectly aligned fiber families. However, experimental evidence suggests that many fiber-reinforced tissues exhibit local dispersion, which can significantly influence their mechanical behavior. Here, we integrate the generalized structure tensor approach into automated material model discovery to represent fibers that are distributed with rotational symmetry around three mean orthogonal directions-fiber, sheet, and normal-by using probabilistic descriptions of the orientation. Using biaxial extension and triaxial shear data from human myocardium, we systematically vary the degree of directional dispersion and stress measurement noise to explore the robustness of the discovered models. Our findings reveal that up to a moderate dispersion in the fiber direction and arbitrary dispersion in the sheet and normal directions improve the goodness of fit and enable recovery of a previously proposed four-term model in terms of the isotropic second invariant, two dispersed anisotropic invariants, and one coupling invariant. Our approach demonstrates strong robustness and consistently identifies similar model terms, even in the presence of up to 7% random noise in the stress data. In summary, our study suggests that automated model discovery based on the powerful generalized structure tensors is robust to noise and captures microstructural uncertainty and heterogeneity in a physiologically meaningful way.

We propose Material Fingerprinting, a new method for the rapid discovery of mechanical material models from direct or indirect data that avoids solving potentially non-convex optimization problems. The core assumption of Material Fingerprinting is that each material exhibits a unique response when subjected to a standardized experimental setup. We can interpret this response as the material's fingerprint, essentially a unique identifier that encodes all pertinent information about the material's mechanical characteristics. Consequently, once we have established a database containing fingerprints and their corresponding mechanical models during an offline phase, we can rapidly characterize an unseen material in an online phase. This is accomplished by measuring its fingerprint and employing a pattern recognition algorithm to identify the best matching fingerprint in the database. In our study, we explore this concept in the context of hyperelastic materials, demonstrating the applicability of Material Fingerprinting across different experimental setups. Initially, we examine Material Fingerprinting through experiments involving homogeneous deformation fields, which provide direct strain-stress data pairs. We then extend this concept to experiments involving complexly shaped specimens with heterogeneous deformation fields, which provide indirect displacement and reaction force measurements. We show that, in both cases, Material Fingerprinting is an efficient tool for model discovery, bypassing the challenges of potentially non-convex optimization. We believe that Material Fingerprinting provides a powerful and generalizable framework for rapid material model identification across a wide range of experimental designs and material behaviors, paving the way for numerous future developments.

Understanding the mechanical behavior of brain tissue is crucial for advancing both fundamental neuroscience and clinical applications. Yet, accurately measuring these properties remains challenging due to the brain's unique mechanical attributes and complex anatomical structures. This review provides a comprehensive overview of commonly used techniques for characterizing brain tissue mechanical properties, covering both invasive methods-such as atomic force microscopy, indentation, axial mechanical testing, and oscillatory shear testing-and noninvasive approaches like magnetic resonance elastography and ultrasound elastography. Each technique is evaluated in terms of working principles, applicability, representative studies, and experimental limitations. We further summarize existing publications that have used these techniques to measure human brain tissue mechanical properties. With a primary focus on invasive studies, we systematically compare their sample preparation, testing conditions, reported mechanical parameters, and modeling strategies. Key sensitivity factors influencing testing outcomes (e.g., sample size, anatomical location, strain rate, temperature, conditioning, and post-mortem interval) are also discussed. Additionally, selected noninvasive studies are reviewed to assess their potential for in vivo characterization. A comparative discussion between invasive and noninvasive methods, as well as in vivo versus ex vivo testing, is included. This review aims to offer practical guidance for researchers and clinicians in selecting appropriate mechanical testing approaches and contributes a curated dataset to support constitutive modeling of human brain tissue. STATEMENT OF SIGNIFICANCE: Accurate characterization of brain tissue mechanics is essential for both neurological research and the development of predictive biomechanical models. This review synthesizes current experimental approaches used in brain mechanical testing-spanning both invasive and noninvasive methods-with a focus on their principles, applications, and limitations. We further systematically compile and analyze a comprehensive set of invasive studies-supplemented by representative noninvasive reports-on human brain tissue mechanical properties. The collected dataset offers valuable support for constitutive modeling. Additionally, we discuss key factors affecting testing outcomes, offering practical insights to guide the design and interpretation of future brain mechanical research.

Abstract Understanding the physiological condition of the vascular system is critical to explain, treat, and manage vascular disease. Numerous experimental and computational studies characterize the mechanical behavior of arterial tissue under controlled laboratory conditions. However, translating this knowledge into physiologically realistic conditions remains challenging. Key difficulties include selecting suitable and relevant test methods, minimizing uncertainty, and ensuring robust model validation. We present a novel integrative approach to translate laboratory experiments on arterial samples into clinically relevant pressure–diameter behavior. We perform controlled planar-biaxial tests on carotid arteries under three stretch ratios and generate axial and circumferential stress–stretch data to calibrate a fiber-reinforced soft tissue model. Using an analytical thick-walled cylindrical model, we predict subject-specific pressure–diameter behavior, informed by arterial prestretches from ring opening experiments. We systematically compare predictions against extension-inflation experiments on tubes from the same artery by applying controlled pairs of axial stretch and inner pressure, while recording outer diameter. We quantify prediction error in absolute and relative stretch regimes and evaluate the importance of the load-free reference dimensions. Results show how planar-biaxial tests probe different stretch regimes compared to extension-inflation deformations, leading to extrapolation of model predictions. We demonstrate how the constitutive material parameters can be fitted to different biomechanical loading conditions and assess the sensitivity of the simulations to axial stretch and circumferential prestretch. Only when key model parameters are accurately captured and their uncertainty propagated, planar-biaxial stress–stretch data can reliably predict arterial pressure–diameter behavior.

Fungi-based meat is emerging as a promising class of nutritious, sustainable, and minimally processed biomaterials with the potential to complement or replace traditional animal and plant-based meats. However, its mechanical and sensory properties remain largely unknown. Here we characterize the quasi-static and dynamic mechanical behavior of fungi-based steak using multi-axial mechanical testing, rheology, and texture profile analysis. We find that the rate-independent response under quasi-static compression and shear is isotropic, while the rate-dependent response under dynamic compression is markedly anisotropic with stiffnesses and peak forces four times larger cross-plane than in-plane. Automated model discovery reveals that the exponential Demiray model best explains the rate-independent elastic response upon chewing in both directions. The rate-dependent directional stiffening can be linked, at least in part, to the high water content of mushroom root mycelium and to the restricted fluid flow at higher loading rates. Complementary sensory surveys reveal a strong correlation with mechanical metrics and suggest that we perceive the fungi-based steak as more moist, more viscous, and more fibrous than traditional animal- and plant-based meats. Taken together, our findings position fungi-based steak as an attractive, structurally equivalent, and sensorially compelling alternative protein source that is healthy for people and for the planet.

When characterizing materials, it can be important to not only predict their mechanical properties, but also to estimate the probability distribution of these properties across a set of samples. Constitutive neural networks allow for the automated discovery of constitutive models that exactly satisfy physical laws given experimental testing data, but are only capable of predicting the mean stress response. Stochastic methods treat each weight as a random variable and are capable of learning their probability distributions. Bayesian constitutive neural networks combine both methods, but their weights lack physical interpretability and we must sample each weight from a probability distribution to train or evaluate the model. Here we introduce more interpretable networks with fewer parameters, simpler training, and the potential to discover correlated weights: Gaussian constitutive neural networks. We demonstrate the performance of our new Gaussian networks on biaxial testing data, and discover a sparse and interpretable four-term model with correlated weights. Importantly, the discovered distributions of material parameters across a set of samples can serve as priors to discover better constitutive models for new samples with limited data. We anticipate that Gaussian constitutive neural networks are a natural first step towards generative constitutive models informed by physical laws and parameter uncertainty. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

The notion of medical digital twins is gaining popularity both within the scientific community and among the general public; however, much of the recent enthusiasm has occurred in the absence of a consensus on their fundamental make-up. Digital twins originate in the field of engineering, in which a constantly updating virtual copy enables analysis, simulation, and prediction of a real-world object or process. In this Health Policy paper, we evaluate this concept in the context of medicine and outline five key components of the medical digital twin: the patient, data connection, patient-in-silico, interface, and twin synchronisation. We consider how various enabling technologies in multimodal data, artificial intelligence, and mechanistic modelling will pave the way for clinical adoption and provide examples pertaining to oncology and diabetes. We highlight the role of data fusion and the potential of merging artificial intelligence and mechanistic modelling to address the limitations of either the AI or the mechanistic modelling approach used independently. In particular, we highlight how the digital twin concept can support the performance of large language models applied in medicine and its potential to address health-care challenges. We believe that this Health Policy paper will help to guide scientists, clinicians, and policy makers in creating medical digital twins in the future and translating this promising new paradigm from theory into clinical practice.

By 2050, feeding nearly 10 billion people will require transformative changes to ensure nutritious, sustainable food for all. Our current food system is inefficient and unsustainable. Traditional attempts to transform the global food system are too slow to drive innovation at scale. Here we explore the potential of artificial intelligence to reshape the future of food. We review the state of the art in food development, discuss the data needed to define a new food product, and highlight seven challenges where AI can help us design nutritious, delicious, and sustainable foods for all. By leveraging AI to democratize food innovation, we can accelerate the transition to resilient global food systems that meet the urgent challenges of food security, climate change, and planetary health.

Abstract Computational modeling has become an integral tool for understanding the interaction between structural organization and functional behavior in a wide range of biological tissues, including the human myocardium. Traditional constitutive models, and recent models generated by automated model discovery, are often based on the simplifying assumption of perfectly aligned fiber families. However, experimental evidence suggests that many fibrous tissues exhibit local dispersion, which can significantly influence their mechanical behavior. Here, we integrate the generalized structure tensor (GST) approach into automated material model discovery to represent fibers that are distributed with rotational symmetry around three mean orthogonal directions—fiber, sheet, and normal—by using probabilistic descriptions of the orientation. Using biaxial extension and triaxial shear data from human myocardium, we systematically vary the degree of directional dispersion and stress measurement noise to explore the robustness of the discovered models. Our findings reveal that small dispersion in the fiber direction and arbitrary dispersion in the sheet and normal directions improve the goodness of fit and enable recovery of a previously proposed four-term model in terms of the isotropic second invariant, two dispersed anisotropic invariants and one coupling invariant. Our approach demonstrates strong robustness and consistently identifies similar model terms, even in the presence of up to 7% random noise in the stress data. In summary, our study suggests that automated model discovery based on the powerful generalized structure tensors is robust to noise and captures microstructural uncertainty and heterogeneity in a physiologically meaningful way.

Abstract Fungi-based meat is emerging as a promising class of nutritious, sustainable, and minimally processed biomaterials with the potential to complement or replace traditional animal and plant-based meats. However, its mechanical and sensory properties remain largely unknown. Here we characterize the quasi-static and dynamic mechanical behavior of fungi-based steak using multi-axial mechanical testing, rheology, and texture profile analysis. We find that the rate-independent response under quasi-static compression and shear is isotropic, while the rate-dependent response under dynamic compression is markedly anisotropic with stiffnesses and peak forces four times larger cross-plane than in-plane. Automated model discovery reveals that the exponential Demiray model best explains the rate-independent elastic response upon chewing in both directions. The rate-dependent directional stiffening can be linked, at least in part, to the high water content of mushroom root mycelium and to the restricted fluid flow at higher loading rates. Complementary sensory surveys reveal a strong correlation with mechanical metrics and suggest that we perceive the fungi-based steak as more moist, more viscous, and more fibrous than traditional animal- and plant-based meats. Taken together, our findings position fungi-based steak as an attractive, structurally equivalent, and sensorially compelling alternative protein source that is healthy for people and for the planet.

Understanding the mechanical behavior of brain tissue is crucial for advancing both fundamental neuroscience and clinical applications. Yet, accurately measuring these properties remains challenging due to the brain unique mechanical attributes and complex anatomical structures. This review provides a comprehensive overview of commonly used techniques for characterizing brain tissue mechanical properties, covering both invasive methods such as atomic force microscopy, indentation, axial mechanical testing, and oscillatory shear testing and noninvasive approaches like magnetic resonance elastography and ultrasound elastography. Each technique is evaluated in terms of working principles, applicability, representative studies, and experimental limitations. We further summarize existing publications that have used these techniques to measure human brain tissue mechanical properties. With a primary focus on invasive studies, we systematically compare their sample preparation, testing conditions, reported mechanical parameters, and modeling strategies. Key sensitivity factors influencing testing outcomes (e.g., sample size, anatomical location, strain rate, temperature, conditioning, and post-mortem interval) are also discussed. Additionally, selected noninvasive studies are reviewed to assess their potential for in vivo characterization. A comparative discussion between invasive and noninvasive methods, as well as in vivo versus ex vivo testing, is included. This review aims to offer practical guidance for researchers and clinicians in selecting appropriate mechanical testing approaches and contributes a curated dataset to support constitutive modeling of human brain tissue.

This work presents a novel approach for characterizing the mechanical behavior of atrial tissue using constitutive neural networks. Based on experimental biaxial tensile test data of healthy human atria, we automatically discover the most appropriate constitutive material model, thereby overcoming the limitations of traditional, pre-defined models. This approach offers a new perspective on modeling atrial mechanics and is a significant step towards improved simulation and prediction of cardiac health.

Abstract Animal agriculture is one of the largest contributors to global carbon emissions. Plant-based meats offer a sustainable alternative to animal meat; yet, people are reluctant to switch their diets and spending habits, in large due to the taste and texture of plant-based meats. Deli meat is a convenient form of protein commonly used in sandwiches, yet little is known about its material or sensory properties. Here we performed biaxial testing with multiple different stretch ratios of four plant-based and four animal deli meats and fit accurate material models to the resulting stress-stretch data. Strikingly, the plant-based products, turkey, ham, deli, and prosciutto, with stiffnesses of 378 ± 15 kPa, 343 ± 62 kPa, 213 ± 25 kPa, and 113 ± 56 kPa, were more than twice as stiff as their animal counterparts, turkey, chicken, ham, and prosciutto, with 134 ± 46 kPa, 117 ± 17 kPa, 117 ± 21 kPa, and 49 ± 21 kPa. In a complementary sensory texture survey, n = 18 participants were able to correlate the physical stiffness with the sensory brittleness, with Spearman’s correlation coefficient of ρ = 0.857 and p = 0.011, but not with the sensory softness or hardness. Notably, the participants perceived all four plant-based products as less fibrous, less moist, and less meaty than the four animal products. Our study confirms the common belief that plant-based products struggle to meet the physical and sensory signature of animal deli meats. We anticipate that integrating rigorous mechanical testing, physics-based modeling, and sensory texture surveys could shape the path towards designing delicious, nutritious, and environmentally friendly meats that mimic the texture and mouthfeel of animal products and are healthy for people and for the planet. Data and code are freely available at https://github.com/LivingMatterLab/CANN .

Accurate modeling of cardiovascular tissues is crucial for understanding and predicting their behavior in various physiological and pathological conditions. In this study, we specifically focus on the pulmonary artery in the context of the Ross procedure, using neural networks to discover the most suitable material model. The Ross procedure is a complex cardiac surgery where the patient's own pulmonary valve is used to replace the diseased aortic valve. Ensuring the successful long-term outcomes of this intervention requires a detailed understanding of the mechanical properties of pulmonary tissue. Constitutive artificial neural networks offer a novel approach to capture such complex stress-strain relationships. Here, we design and train different constitutive neural networks to characterize the hyperelastic, anisotropic behavior of the main pulmonary artery. Informed by experimental biaxial testing data under various axial-circumferential loading ratios, these networks autonomously discover the inherent material behavior, without the limitations of predefined mathematical models. We regularize the model discovery using cross-sample feature selection and explore its sensitivity to the collagen fiber distribution. Strikingly, we uniformly discover an isotropic exponential first-invariant term and an anisotropic quadratic fifth-invariant term. We show that constitutive models with both these terms can reliably predict arterial responses under diverse loading conditions. Our results provide crucial improvements in experimental data agreement, and enhance our understanding into the biomechanical properties of pulmonary tissue. The model outcomes can be used in a variety of computational frameworks of autograft adaptation, ultimately improving the surgical outcomes after the Ross procedure.

Abnormal passive stiffness of the heart muscle (myocardium) is evident in the pathophysiology of several cardiovascular diseases, making it an important indicator of heart health. Recent advancements in cardiac imaging and biophysical modeling now enable more effective evaluation of this biomarker. Estimating passive myocardial stiffness can be accomplished through an MRI-based approach that requires comprehensive subject-specific input data. This includes the gross cardiac geometry (e.g. from conventional cine imaging), regional diastolic kinematics (e.g. from tagged MRI), microstructural configuration (e.g. from diffusion tensor imaging), and ventricular diastolic pressure, whether invasively measured or non-invasively estimated. Despite the progress in cardiac biomechanics simulations, developing a framework to integrate multiphase and multimodal cardiac MRI data for estimating passive myocardial stiffness has remained a challenge. Moreover, the sensitivity of estimated passive myocardial stiffness to input data has not been fully explored. This study aims to: (1) develop a framework for integrating subject-specific in vivo MRI data into in silico left ventricular finite element models to estimate passive myocardial stiffness, (2) apply the framework to estimate the passive myocardial stiffness of multiple healthy subjects under assumed filling pressure, and (3) assess the sensitivity of these estimates to loading conditions and myofiber orientations. This work contributes toward the establishment of a range of reference values for material parameters of passive myocardium in healthy human subjects. Notably, in this study, beat-to-beat variation in left ventricular end-diastolic pressure was found to have a greater influence on passive myocardial material parameter estimation than variation in fiber orientation.

• To mimic animal meat, plant-based meat must match mouthfeel, taste, and texture. • To quantify texture, we tested eight meats using texture profile analysis and rheology. • Sample stiffnesses varied from 419 kPa for plant-based turkey to 57 kPa for tofu. • Animal turkey, sausage, and hotdog ranked within these plant-based extremes. • Plant-based meat can replicate the full stiffness spectrum of comminuted animal meat. Plant-based meat can help combat climate change and health risks associated with high meat consumption. To create adequate mimics of animal meats, plant-based meats must match in mouthfeel, taste, and texture. The gold standard to characterize the texture of meat is the double compression test, but this test suffers from a lack of standardization and reporting inconsistencies. Here we characterize the texture of five plant-based and three animal meats using texture profile analysis and rheology, and report ten mechanical features associated with each product’s elasticity, viscosity, and loss of integrity. Our findings suggest that, of all ten features, the stiffness, storage, and loss moduli are the most meaningful and consistent parameter to report, while other parameters suffer from a lack of interpretability and inconsistent definitions. We find that the sample stiffness varies by an order of magnitude, from 418.9 ± 41.7 kPa for plant-based turkey to 56.7 ± 14.1 kPa for tofu. Similarly, the storage and loss moduli vary from 50.4 ± 4.1 kPa and 25.3 ± 3.0 kPa for plant-based turkey to 5.7 ± 0.5 kPa and 1.3 ± 0.1 kPa for tofu. All three animal products, animal turkey, sausage, and hotdog, consistently rank in between these two extremes. Our results suggest that–with the right ingredients, additives, and formulation–modern food fabrication techniques can create plant-based meats that successfully replicate the full viscoelastic texture spectrum of processed animal meat.

We present a built-in physics neural network architecture, known as inelastic Constitutive Artificial Neural Network (iCANN), to discover the inelastic phenomenon of tensional homeostasis. In this course, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. We introduce the incorporation of kinematic growth and homeostatic surfaces into the iCANN to discover the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. To this end, we additionally propose a novel design of the corresponding feed-forward network in terms of principal stresses. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282 . • New iCANN framework for model discovery in growth and remodeling • The framework captures finite deformations, rates, and satisfies thermodynamics. • The pseudo potential/homeostatic surface is based on principal and shear stresses. • Specific activation functions are introduced to discover tensional homeostasis. • Discovery of experimental data for tissue equivalents.

Animal agriculture is one of the largest contributors to global carbon emissions. Plant-based meats offer a sustainable alternative to animal meat; yet, people are reluctant to switch their diets and spending habits, in large due to the taste and texture of plant-based meats. Deli meat is a convenient form of protein commonly used in sandwiches, yet little is known about its material or sensory properties. Here we performed biaxial testing with multiple different stretch ratios of four plant-based and four animal deli meats, fit the neo Hooke and Mooney Rivlin models to the resulting stress–stretch data, and discovered the best constitutive models for all eight products. Strikingly, the plant-based products, turkey, ham, deli, and prosciutto, with stiffnesses of 378 ± 15 kPa, 343 ± 62 kPa, 213 ± 25 kPa, and 113 ± 56 kPa, were more than twice as stiff as their animal counterparts, turkey, chicken, ham, and prosciutto, with 134 ± 46 kPa, 117 ± 17 kPa, 117 ± 21 kPa, and 49 ± 21 kPa. In a complementary sensory texture survey, n = 18 participants were able to correlate the physical stiffness with the sensory brittleness, with Spearman’s correlation coefficient of ρ = 0 . 857 and p = 0 . 011 , but not with the sensory softness or hardness. Notably, the participants perceived all four plant-based products as less fibrous, less moist, and less meaty than the four animal products. Our study confirms the common belief that plant-based products struggle to meet the physical and sensory signature of animal deli meats. We anticipate that integrating rigorous mechanical testing, physics-based modeling, and sensory texture surveys could shape the path towards designing delicious, nutritious, and environmentally friendly meats that mimic the texture and mouthfeel of animal products and are healthy for people and for the planet. Data and code are freely available at https://github.com/LivingMatterLab/CANN .

Data-driven approaches have led to structured constitutive artificial neural network formulations for inelastic phenomena such as viscoelasticity and growth, while the systematic extension to finite-strain plasticity remains an active area of research. In this communication, we extend the previously introduced inelastic constitutive artificial neural network framework to finite-strain elasto-visco-plasticity with combined nonlinear kinematic and isotropic hardening. The proposed formulation ensures thermodynamic consistency within a potential-based architecture by consistently integrating isotropic hardening and viscoplastic evolution mechanisms. In particular, a shared inelastic potential is employed for linear kinematic and isotropic hardening, while two additional potentials govern nonlinear kinematic hardening and the plastic yield function, enabling the modeling of non-associative plasticity. A JAX implementation of the extended framework and the associated simulation results are publicly available at Zenodo.org.