Michael P. Brenner

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules self-organize by phase transitions into coexisting spatial compartments called condensates, often on cellular surfaces such as chromatin and membranes. In this paper, we demonstrate that multicomponent fluids can be designed to recruit distinct condensates to surfaces with differing compositions, performing a form of surface classification by condensation. We draw an analogy to multidimensional classification in machine learning and explore how hidden species, analogous to hidden nodes, expand the expressivity and capacity of these interacting ensembles to facilitate complex decision boundaries. By simply changing levels of individual species, we find that the same molecular repertoire can be reprogrammed to solve new tasks. Together, our findings suggest that the physical processes underlying biomolecular condensates can encode and drive adaptive information processing beyond compartmentalization.

Version 2: Added missing files to sniffing_data.zip See GitHub repository for data processing functions and examples: https://github.com/soerenbrandt/sniffing-sensor Abstract:Sensor technologies have allowed us to outperform the human senses of sight, hearing, and touch; however, the development of artificial noses is significantly behind their biological counterparts. This is largely due to the complexity of natural olfaction, as it incorporates complex fluid dynamics within the nasal anatomy together with the response patterns of hundreds to thousands of unique molecular-scale receptors for odor interpretation. We designed a sensing approach to identify volatiles that exploits time-dependent information from a single sensor (here, the reflectance spectra from a mesoporous one-dimensional photonic crystal) by augmenting and accentuating differences in the non-equilibrium mass-transport dynamics of vapors stemming from their distinct physicochemical properties, thus obviating the need for a large sensor array. By training a machine learning algorithm on the sensor output, we clearly identify polar and nonpolar volatile organic compounds, determine the mixing ratios of binary mixtures, and accurately predict the boiling point, flash point, vapor pressure, and viscosity of several volatile liquids within those used for training as well as compounds unknown to the model. We further implement a bioinspired active sniffing approach, in which the fluid dynamics and patterns of analyte delivery are controlled, enabling an additional modality of differentiation and reducing the duration of data collection and analysis to seconds. These results outline a strategy to build accurate and rapid artificial noses for volatile liquids that can provide useful information on chemicals such as their composition and properties, and can be applied in a variety of fields, including disease diagnosis, hazardous waste management, and healthy building monitoring.

Large Language Models (LLMs) show great promise as a powerful tool for scientific literature exploration. However, their effectiveness in providing scientifically accurate and comprehensive answers to complex questions within specialized domains remains an active area of research. Using the field of high-temperature cuprates as an exemplar, we evaluate the ability of LLM systems to understand the literature at the level of an expert. We construct an expert-curated database of 1,726 scientific papers that covers the history of the field, and a set of 67 expert-formulated questions that probe deep understanding of the literature. We then evaluate six different LLM-based systems for answering these questions, including both commercially available closed models and a custom retrieval-augmented generation (RAG) system capable of retrieving images alongside text. Experts then evaluate the answers of these systems against a rubric that assesses balanced perspectives, factual comprehensiveness, succinctness, and evidentiary support. Among the six systems, two using RAG on curated literature outperformed existing closed models across key metrics, particularly in providing comprehensive and well-supported answers. We discuss promising aspects of LLM performances as well as critical short-comings of all the models. The set of expert-formulated questions and the rubric will be valuable for assessing expert level performance of LLM based reasoning systems.

Large Language Models (LLMs) offer a framework for understanding language processing in the human brain. Unlike traditional models, LLMs represent words and context through layered numerical embeddings. Here, we demonstrate that LLMs' layer hierarchy aligns with the temporal dynamics of language comprehension in the brain. Using electrocorticography (ECoG) data from participants listening to a 30-minute narrative, we show that deeper LLM layers correspond to later brain activity, particularly in Broca's area and other language-related regions. We extract contextual embeddings from GPT-2 XL and Llama-2 and use linear models to predict neural responses across time. Our results reveal a strong correlation between model depth and the brain's temporal receptive window during comprehension. We also compare LLM-based predictions with symbolic approaches, highlighting the advantages of deep learning models in capturing brain dynamics. We release our aligned neural and linguistic dataset as a public benchmark to test competing theories of language processing.

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, conditioning a neural model on a vector encoding representing the terms in a PDE and their coefficients. We present a baseline of four distinct modeling technqiues, trained on a family of 1D PDEs from the APEBench suite. Our approach achieves strong performance on parameter sets held out from the training distribution, with strong stability for rollout beyond the training window, and generalization to an entirely unseen PDE. This work was developed as part of a broader effort exploring AI systems that automate the creation of expert-level empirical software for scorable scientific tasks. The data and codebase are available at https://github.com/google-research/generalized-pde-emulator.

Abstract Differential adhesion, where cells physically reorganize based on their heterogeneous adhesion preferences, is one of the major models for self-organization in development and tissue formation. However, accumulating evidence suggests that differential adhesion is many times insufficient for robust convergence to a target minimal energy multicellular structure. Here we use computational simulations and engineered synthetic cell circuits to systematically explore alternative mechanisms for programming formation of a simple two-cell type core-shell morphology. Starting with two pre-differentiated cell types with constitutively high differential adhesion leads to kinetic trapping in variable, multi-core structures. In contrast, hybrid mechanisms that gradually induce differential adhesion upon cell-cell contact signaling consistently converge to the target single-core structure, in a manner robust to variation in cell numbers, interaction energy, and noise. This work delineates intrinsic limitations of self-organizing systems based solely on differential adhesion, and shows how inducible systems provide a way to invoke the strong adhesion required to maintain a multicellular structure, while avoiding the pitfall of kinetic traps. This study illustrates how joint computational and experimental exploration of synthetic circuits can be used to probe key developmental principles and tradeoffs and inform the design of synthetic development and self-organization.

Designing heterogeneous, self-assembling systems is a central challenge in soft matter and biology. We present a framework that uses gradient-based optimization to invert an analytical yield calculation, tuning systems toward target equilibrium yields. We design systems ranging from simple dimers to temperature-controlled shells to polymerizing systems, achieving precise control of self- and non-self-limiting assemblies. By operating directly on closed-form calculations, our framework bypasses trajectory-based instabilities and enables efficient optimization in otherwise challenging regimes.

Life thrives due to its remarkable ability to create complex structures through the self-assembly of proteins, nucleic acids, and other biomolecules. Achieving such complex assemblies with the same level of fidelity, reproducibility, and advanced functionality in synthetic systems, however, has remained a grand challenge. One outstanding problem is the presence of parasitic products and long-lived intermediate states that slow the reaction process and limit the yield of the final product. Biology overcomes this challenge by proofreading to recognize and disassemble parasitic products. Such local checks, however, are currently difficult to implement in available self-assembly platforms. Here, we overcome this challenge by implementing a proofreading mechanism in a self-assembly platform. Specifically, we design intermediate states that strongly couple to an external force but a final product that is decoupled and thus highly stable to external driving, such that application of external forces selectively dissociates parasitic products. To implement this idea, we introduce lithographically patterned magnetic dipoles and an applied magnetic field to drive an assembly process similar to thermal self-assembly, but with additional controls. By applying patterns of magnetic driving that selectively destabilize parasitic states, we effectively implement a proofreading strategy to enable high-yield, time-efficient self-assembly. This realization of a general proofreading mechanism bridges the gap between artificial and biological self-assembly, paving the way for advanced self-assembled materials, with applications in next generation responsive materials, biomimetic devices, and microscale machines.

Understanding the fundamental rules of organismal development is a central, unsolved problem in biology. These rules dictate how individual cellular actions coordinate over macroscopic numbers of cells to grow complex structures with exquisite functionality. We use recent advances in automatic differentiation to discover local interaction rules and genetic networks that yield emergent, systems-level characteristics in a model of development. We consider a growing tissue with cellular interactions mediated by morphogen diffusion, cell adhesion and mechanical stress. Each cell has an internal genetic network that is used to make decisions based on the cell’s local environment. Here we show that one can learn the parameters governing cell interactions in the form of interpretable genetic networks for complex developmental scenarios. When combined with recent experimental advances measuring spatio-temporal dynamics and gene expression of cells in a growing tissue, the methodology outlined here offers a promising path to unraveling the cellular bases of development. This work uses differentiable simulations and reinforcement learning to design interpretable genetic networks, enabling simulated cells to self-organize into emergent developmental patterns by responding to local chemical and mechanical cues.

We describe a DNA-array-based method to infer intramolecular connections in a population of RNA molecules in vitro. First we add DNA oligonucleotide "patches" that perturb the RNA connections, and then we use a microarray containing a complete set of DNA oligonucleotide "probes" to record where perturbations occur. The pattern of perturbations reveals couplings between regions of the RNA sequence, from which we infer connections as well as their prevalences in the population, without reference to folding models. We validate this patch-probe method using the 1058-nucleotide RNA genome of satellite tobacco mosaic virus (STMV), which has been shown to have multiple long-range connections. Our results not only indicate long-range connections that agree with previous structures but also reveal the prevalence of competing connections. Together, these results suggest that multiple structures with different connectivity coexist in solution. Furthermore, we show that the prevalence of certain connections changes when pseudouridine, an important component of natural and synthetic RNAs, is substituted for uridine in STMV RNA, and that the connectivity of STMV minus strands is qualitatively distinct from that of plus strands. Finally, we use a simplified version of the method to validate a predicted 317-nucleotide connection within the 3569-nucleotide RNA genome of bacteriophage MS2.

Through programmable self-assembly, simple building blocks can be made to form highly complex structures following local rules of interaction. However, materials systems that are most commonly utilized for programmable assembly often lack interactions that exhibit the strength, specificity, and long ranges, which would, as a result, allow for robust and rapid hierarchical self-assembly processes. "Magnetic handshake" building blocks resolve many of these challenges at once, incorporating strong, long-range, and specific magnetic interactions through patterning of magnetic dipoles onto rigid panels. When appropriately designed, the panels organize hierarchically: first into chains, and subsequently those chains combine to form dense stacks. Here, we examine differences in phase behavior and morphology for four panel types. We delineate how perpendicular chaining and stacking interactions between panels compete and how they can be manipulated to reverse the sequence of the hierarchical assembly pathway. Collectively, our work shows the enormous potential for using magnetic handshake materials for self-assembly of hierarchically organized complex structures.

Building precise simulations of the real world and invoking numerical solvers to answer quantitative problems is an essential requirement in engineering and science. We present FEABench, a benchmark to evaluate the ability of large language models (LLMs) and LLM agents to simulate and solve physics, mathematics and engineering problems using finite element analysis (FEA). We introduce a comprehensive evaluation scheme to investigate the ability of LLMs to solve these problems end-to-end by reasoning over natural language problem descriptions and operating COMSOL Multiphysics$^\circledR$, an FEA software, to compute the answers. We additionally design a language model agent equipped with the ability to interact with the software through its Application Programming Interface (API), examine its outputs and use tools to improve its solutions over multiple iterations. Our best performing strategy generates executable API calls 88% of the time. LLMs that can successfully interact with and operate FEA software to solve problems such as those in our benchmark would push the frontiers of automation in engineering. Acquiring this capability would augment LLMs' reasoning skills with the precision of numerical solvers and advance the development of autonomous systems that can tackle complex problems in the real world. The code is available at https://github.com/google/feabench

This study introduces a unified computational framework connecting acoustic, speech and word-level linguistic structures to study the neural basis of everyday conversations in the human brain. We used electrocorticography to record neural signals across 100 h of speech production and comprehension as participants engaged in open-ended real-life conversations. We extracted low-level acoustic, mid-level speech and contextual word embeddings from a multimodal speech-to-text model (Whisper). We developed encoding models that linearly map these embeddings onto brain activity during speech production and comprehension. Remarkably, this model accurately predicts neural activity at each level of the language processing hierarchy across hours of new conversations not used in training the model. The internal processing hierarchy in the model is aligned with the cortical hierarchy for speech and language processing, where sensory and motor regions better align with the model's speech embeddings, and higher-level language areas better align with the model's language embeddings. The Whisper model captures the temporal sequence of language-to-speech encoding before word articulation (speech production) and speech-to-language encoding post articulation (speech comprehension). The embeddings learned by this model outperform symbolic models in capturing neural activity supporting natural speech and language. These findings support a paradigm shift towards unified computational models that capture the entire processing hierarchy for speech comprehension and production in real-world conversations.

Inverse design of complex flows is notoriously challenging because of the high cost of high dimensional optimization. Usually, optimization problems are either restricted to few control parameters, or adjoint-based approaches are used to convert the optimization problem into a boundary value problem. Here, we show that the recent advances in automatic differentiation (AD) provide a generic platform for solving inverse problems in complex fluids. To demonstrate the versatility of the approach, we solve an array of optimization problems related to active matter motion in Newtonian fluids, dispersion in structured porous media, and mixing in journal bearing. Each of these problems highlights the advantages of AD in ease of implementation and computational efficiency to solve high-dimensional optimization problems involving particle-laden flows.

Abstract Large language models (LLMs) have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. We demonstrate that with carefully designed prompts, LLMs can accurately carry out key calculations in research papers in theoretical physics. We focus on a broadly-used approximation method in quantum physics: the Hartree-Fock method, requiring an analytic multi-step calculation deriving approximate Hamiltonian and corresponding self-consistency equations. To carry out the calculations using LLMs, we design multi-step prompt templates that break down the analytic calculation into standardized steps with placeholders for problem-specific information. We evaluate GPT-4’s performance in executing the calculation for 15 papers from the past decade, demonstrating that, with the correction of intermediate steps, it can correctly derive the final Hartree-Fock Hamiltonian in 13 cases. Aggregating across all research papers, we find an average score of 87.5 (out of 100) on the execution of individual calculation steps. We further use LLMs to mitigate the two primary bottlenecks in this evaluation process: (i) extracting information from papers to fill in templates and (ii) automatic scoring of the calculation steps, demonstrating good results in both cases.

Daniel J. Liebling, Malcolm Kane, Madeleine Grunde-McLaughlin, Ian Lang, Subhashini Venugopalan, Michael Brenner. Proceedings of the 1st Workshop on AI and Scientific Discovery: Directions and Opportunities. 2025.

In the version of the article initially published, there was an error in the Fig. 4b,c caption, now reading “Plasma bubbles in the equatorial anomaly over South America at 00:20 on 13 October 2023,” where 13 October 2023 appeared originally as “13 May 2024.” The error has been corrected in the HTML and PDF versions of the article.

Designing components that can robustly self-assemble into structures with biological complexity is a grand challenge for material science. Proofreading and error correction is required to improve assembly yield beyond equilibrium limits, using energy to avoid kinetic traps in the energy landscape. Here, we introduce an explicit two-staged proofreading scheme for patchy particle colloidal assemblies that substantially improves assembly yield and robustness. The first stage implements local rules whereby particles increase their binding strengths when they detect a local environment corresponding to a desired target. The second stage corrects remaining errors, adding a reverse pathway inspired by kinetic proofreading. The scheme shows significant yield improvements, eliminating kinetic traps, giving a much broader temperature range with high yield. Additionally, the scheme is robust against quenched disorder in the components. Our findings illuminate a pathway for advancing the programmable design of synthetic living materials, potentially fostering the synthesis of novel biological materials and functional behaviors. Published by the American Physical Society 2024

The precise control of complex reactions is critical for biological processes, yet our inability to design for specific outcomes limits the development of synthetic analogs. Here, we leverage differentiable simulators to design nontrivial reaction pathways in colloidal assemblies. By optimizing over external structures, we achieve controlled disassembly and particle release from colloidal shells. Lastly, we characterize the role of configurational entropy in the structure via both forward calculations and optimization, inspiring new parameterizations of designed colloidal reactions.

Developing physics-based models for molecular simulation requires fitting many unknown parameters to diverse experimental datasets. Traditionally, this process is piecemeal and difficult to reproduce, leading to a fragmented landscape of models. Here, we establish a systematic, extensible framework for fitting coarse-grained molecular models to macroscopic experimental data by leveraging recently developed methods for computing low-variance gradient estimates with automatic differentiation. Using a widely validated DNA force field as an exemplar, we develop methods for optimizing structural, mechanical, and thermodynamic properties across a range of simulation techniques, including enhanced sampling and external forcing, spanning micro- and millisecond timescales. We highlight how gradients enable efficient sensitivity analyses that yield physical insight. We then demonstrate the broad applicability of these techniques by optimizing diverse biomolecular systems, including RNA and DNA-protein hybrid models. We show how conflict-free gradient methods from multi-task learning can be adapted to impose multiple constraints simultaneously without compromising accuracy. This approach provides a foundation for transparent, reproducible, community-driven force field development, accelerating progress in molecular modeling.

Abstract The ionosphere is a layer of weakly ionized plasma bathed in Earth’s geomagnetic field extending about 50–1,500 kilometres above Earth 1 . The ionospheric total electron content varies in response to Earth’s space environment, interfering with Global Satellite Navigation System (GNSS) signals, resulting in one of the largest sources of error for position, navigation and timing services 2 . Networks of high-quality ground-based GNSS stations provide maps of ionospheric total electron content to correct these errors, but large spatiotemporal gaps in data from these stations mean that these maps may contain errors 3 . Here we demonstrate that a distributed network of noisy sensors—in the form of millions of Android phones—can fill in many of these gaps and double the measurement coverage, providing an accurate picture of the ionosphere in areas of the world underserved by conventional infrastructure. Using smartphone measurements, we resolve features such as plasma bubbles over India and South America, solar-storm-enhanced density over North America and a mid-latitude ionospheric trough over Europe. We also show that the resulting ionosphere maps can improve location accuracy, which is our primary aim. This work demonstrates the potential of using a large distributed network of smartphones as a powerful scientific instrument for monitoring Earth.

Accelerating text input in augmentative and alternative communication (AAC) is a long-standing area of research with bearings on the quality of life in individuals with profound motor impairments. Recent advances in large language models (LLMs) pose opportunities for re-thinking strategies for enhanced text entry in AAC. In this paper, we present SpeakFaster, consisting of an LLM-powered user interface for text entry in a highly-abbreviated form, saving 57% more motor actions than traditional predictive keyboards in offline simulation. A pilot study on a mobile device with 19 non-AAC participants demonstrated motor savings in line with simulation and relatively small changes in typing speed. Lab and field testing on two eye-gaze AAC users with amyotrophic lateral sclerosis demonstrated text-entry rates 29-60% above baselines, due to significant saving of expensive keystrokes based on LLM predictions. These findings form a foundation for further exploration of LLM-assisted text entry in AAC and other user interfaces.

The design of folded proteins has advanced significantly in recent years. However, many proteins and protein regions are intrinsically disordered (IDPs) and lack a stable fold i.e., the sequence of an IDP encodes a vast ensemble of spatial conformations that specify its biological function. This conformational plasticity and heterogeneity makes IDP design challenging. Here, we introduce a computational framework for de novo design of IDPs through rational and efficient inversion of molecular simulations that approximate the underlying sequence to ensemble relationship. We highlight the versatility of this approach by designing IDPs with diverse properties and arbitrary sequence constraints. These include IDPs with target ensemble dimensions, loops and linkers, highly sensitive sensors of physicochemical stimuli, and binders to target disordered substrates with distinct conformational biases. Overall, our method provides a general framework for designing sequence-ensemble-function relationships of biological macromolecules.

The original author list was: Ariel Goldstein, Avigail Grinstein-Dabush, Mariano Schain, Haocheng Wang, Zhuoqiao Hong, Bobbi Aubrey, Mariano Schain, Samuel A. Nastase, Zaid Zada, Eric Ham, Amir Feder, Harshvardhan Gazula, Eliav Buchnik, Werner Doyle, Sasha Devore, Patricia Dugan, Roi Reichart, Daniel Friedman, Michael Brenner, Avinatan Hassidim, Orrin Devinsky, Adeen Flinker & Uri Hasson

Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$ . ‘Latent Fourier analysis’ (Page et al. , Phys. Rev. Fluids 6 , 2021, p. 034402) reveals a detached class of bursting dynamics at $Re=40$ which merge with the low-dissipation dynamics as $Re$ is increased to $100$ and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At $Re=400$ , the UPOs discovered at lower $Re$ move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier projections identify an associated ‘large-scale’ UPO which we believe to be a finite- $Re$ continuation of a solution to the Euler equations.

Abstract General circulation models (GCMs) are the foundation of weather and climate prediction 1,2 . GCMs are physics-based simulators that combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine-learning models trained on reanalysis data have achieved comparable or better skill than GCMs for deterministic weather forecasting 3,4 . However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present a GCM that combines a differentiable solver for atmospheric dynamics with machine-learning components and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best machine-learning and physics-based methods. NeuralGCM is competitive with machine-learning models for one- to ten-day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for one- to fifteen-day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics for multiple decades, and climate forecasts with 140-kilometre resolution show emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs, although our model does not extrapolate to substantially different future climates. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how these individual actions coordinate over a macroscopic number of cells to grow complex structures with exquisite functionality is unknown. Here we use recent advances in automatic differentiation to discover local interaction rules and genetic networks that yield emergent, systems-level characteristics in a model of development. We consider a growing tissue with cellular interactions mediated by morphogen diffusion, cell adhesion and mechanical stress. Each cell has an internal genetic network that is used to make decisions based on the cell's local environment. We show that one can learn the parameters governing cell interactions in the form of interpretable genetic networks for complex developmental scenarios, including directed axial elongation, cell type homeostasis via chemical signaling and homogenization of growth via mechanical stress. When combined with recent experimental advances measuring spatio-temporal dynamics and gene expression of cells in a growing tissue, the methodology outlined here offers a promising path to unraveling the cellular bases of development.

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps toward designing functional materials have proven challenging. If the material is constructed from highly complex components, the design space of materials properties rapidly becomes too computationally expensive to search. On the other hand, very simple components such as uniform spherical particles are not powerful enough to capture rich functional behavior. Here, we introduce a differentiable materials design model with components that are simple enough to design yet powerful enough to capture complex materials properties: rigid bodies composed of spherical particles with directional interactions (patchy particles). We showcase the method with self-assembly designs ranging from open lattices to self-limiting clusters, all of which are notoriously challenging design goals to achieve using purely isotropic particles. By directly optimizing over the location and interaction of the patches on patchy particles using gradient descent, we dramatically reduce the computation time for finding the optimal building blocks.

, 303 (1948)]. The chaotic dynamics are shaped by the unstable simple invariant solutions populating the inertial manifold. The hope has been to turn this picture into a predictive framework where the statistics of the flow follow from a weighted sum of the statistics of each simple invariant solution. Two outstanding obstacles have prevented this goal from being achieved: 1) paucity of known solutions and 2) the lack of a rational theory for predicting the required weights. Here, we describe a method to substantially solve these problems, and thereby provide compelling evidence that the probability density functions (PDFs) of a fully developed turbulent flow can be reconstructed with a set of unstable periodic orbits. Our method for finding solutions uses automatic differentiation, with high-quality guesses constructed by minimizing a trajectory-dependent loss function. We use this approach to find hundreds of solutions in turbulent, two-dimensional Kolmogorov flow. Robust statistical predictions are then computed by learning weights after converting a turbulent trajectory into a Markov chain for which the states are individual solutions, and the nearest solution to a given snapshot is determined using a deep convolutional autoencoder. In this study, the PDFs of a spatiotemporally chaotic system have been successfully reproduced with a set of simple invariant states, and we provide a fascinating connection between self-sustaining dynamical processes and the more well-known statistical properties of turbulence.

Recent advancements in automatic differentiation, which played a pivotal role in deep learning, offer a promising approach to addressing challenges in controlling fluid flow behavior. We demonstrate the power of the method by optimizing the packing of a polydisperse system of periodically arranged circular rods to minimize the pressure drop across the media. We show how the optimum topology of the porous media changes with changing the packing fraction.

Contextual embeddings, derived from deep language models (DLMs), provide a continuous vectorial representation of language. This embedding space differs fundamentally from the symbolic representations posited by traditional psycholinguistics. We hypothesize that language areas in the human brain, similar to DLMs, rely on a continuous embedding space to represent language. To test this hypothesis, we densely record the neural activity patterns in the inferior frontal gyrus (IFG) of three participants using dense intracranial arrays while they listened to a 30-minute podcast. From these fine-grained spatiotemporal neural recordings, we derive a continuous vectorial representation for each word (i.e., a brain embedding) in each patient. Using stringent zero-shot mapping we demonstrate that brain embeddings in the IFG and the DLM contextual embedding space have common geometric patterns. The common geometric patterns allow us to predict the brain embedding in IFG of a given left-out word based solely on its geometrical relationship to other non-overlapping words in the podcast. Furthermore, we show that contextual embeddings capture the geometry of IFG embeddings better than static word embeddings. The continuous brain embedding space exposes a vector-based neural code for natural language processing in the human brain.

Large language models (LLMs) have demonstrated an unprecedented ability to perform complex tasks in multiple domains, including mathematical and scientific reasoning. We demonstrate that with carefully designed prompts, LLMs can accurately carry out key calculations in research papers in theoretical physics. We focus on a broadly used approximation method in quantum physics: the Hartree-Fock method, requiring an analytic multi-step calculation deriving approximate Hamiltonian and corresponding self-consistency equations. To carry out the calculations using LLMs, we design multi-step prompt templates that break down the analytic calculation into standardized steps with placeholders for problem-specific information. We evaluate GPT-4's performance in executing the calculation for 15 research papers from the past decade, demonstrating that, with correction of intermediate steps, it can correctly derive the final Hartree-Fock Hamiltonian in 13 cases and makes minor errors in 2 cases. Aggregating across all research papers, we find an average score of 87.5 (out of 100) on the execution of individual calculation steps. Overall, the requisite skill for doing these calculations is at the graduate level in quantum condensed matter theory. We further use LLMs to mitigate the two primary bottlenecks in this evaluation process: (i) extracting information from papers to fill in templates and (ii) automatic scoring of the calculation steps, demonstrating good results in both cases. The strong performance is the first step for developing algorithms that automatically explore theoretical hypotheses at an unprecedented scale.

Soft materials made from braided or woven microscale fibers can display unique properties that can be exploited in electromagnetic, mechanical, and biomedical applications. These properties depend on the topology of the braids or weaves-that is, the order in which fibers cross one another. Current industrial braiding and weaving machines cannot easily braid or weave micrometer-scale fibers into controllable topologies; they typically apply forces that are large enough to break the fibers, and each machine can typically make only one topology. Here we use a 3D-printed device called a "capillary machine" to manipulate micrometer-scale fibers without breaking them. The operating principle is the physics of capillary forces: as the machines move vertically, they exert lateral capillary forces on floating objects, which in turn move small fibers connected to them. We present a new type of capillary machine that is based on principles of braid theory. It implements all the possible fiber-swapping operations for a set of four fibers and can therefore make any four-strand topology, including braids, twists, hierarchical twists, and weaves. We make these different topologies by changing the pattern of vertical motion of the machine. This approach is a mechanically simple, yet versatile way to make micro- and nano-textiles. We describe the prospects and limitations of this new type of machine for applications.

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.

Designing components that can robustly self-assemble into structures with biological complexity is a grand challenge for material science. Proofreading and error correction is required to improve assembly yield beyond equilibrium limits, using energy to avoid kinetic traps in the energy landscape. Here we introduce an explicit two staged proofreading scheme for patchy particle colloidal assemblies that substantially improves assembly yield and robustness. The first stage implements local rules whereby particles increase their binding strengths when they detect a local environment corresponding to a desired target. The second stage corrects remaining errors, adding a reverse pathway inspired by kinetic proofreading. The scheme shows significant yield improvements, eliminating kinetic traps, giving a much broader temperature range with high yield. Additionally, the scheme is robust against quenched disorder in the components. Our findings illuminate a pathway for advancing programmable design of synthetic living materials, potentially fostering the synthesis of novel biological materials and functional behaviors.

Direct design of complex functional materials would revolutionize technologies ranging from printable organs to novel clean energy devices. However, even incremental steps towards designing functional materials have proven challenging. If the material is constructed from highly complex components, the design space of materials properties rapidly becomes too computationally expensive to search. On the other hand, very simple components such as uniform spherical particles are not powerful enough to capture rich functional behavior. Here, we introduce a differentiable materials design model with components that are simple enough to design yet powerful enough to capture complex materials properties: rigid bodies composed of spherical particles with directional interactions (patchy particles). We showcase the method with self-assembly designs ranging from open lattices to self-limiting clusters, all of which are notoriously challenging design goals to achieve using purely isotropic particles. By directly optimizing over the location and interaction of the patches on patchy particles using gradient descent, we dramatically reduce the computation time for finding the optimal building blocks.

Finding ways to accelerate text input for individuals with profound motor impairments has been a long-standing area of research. Closing the speed gap for augmentative and alternative communication (AAC) devices such as eye-tracking keyboards is important for improving the quality of life for such individuals. Recent advances in neural networks of natural language pose new opportunities for re-thinking strategies and user interfaces for enhanced text-entry for AAC users. In this paper, we present SpeakFaster, consisting of large language models (LLMs) and a co-designed user interface for text entry in a highly-abbreviated form, allowing saving 57% more motor actions than traditional predictive keyboards in offline simulation. A pilot study with 19 non-AAC participants typing on a mobile device by hand demonstrated gains in motor savings in line with the offline simulation, while introducing relatively small effects on overall typing speed. Lab and field testing on two eye-gaze typing users with amyotrophic lateral sclerosis (ALS) demonstrated text-entry rates 29-60% faster than traditional baselines, due to significant saving of expensive keystrokes achieved through phrase and word predictions from context-aware LLMs. These findings provide a strong foundation for further exploration of substantially-accelerated text communication for motor-impaired users and demonstrate a direction for applying LLMs to text-based user interfaces.

A new approach to computing optimal nonequilibrium controls applicable to complex systems far from equilibrium, providing a tool for expanded studies into optimized nanotechnology and the evolution of biomolecular systems.