Michael P. Brenner

Gideon Dresdner, Dmitrii Kochkov, Peter Norgaard et al.

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and more recently, a whirlwind of research into data-driven techniques leveraging machine learning (ML). A recent line of work indicates that a hybrid of classical numerical techniques and machine learning can offer significant improvements over either approach alone. In this work, we show that the choice of the numerical scheme is crucial when incorporating physics-based priors. We build upon Fourier-based spectral methods, which are known to be more efficient than other numerical schemes for simulating PDEs with smooth and periodic solutions. Specifically, we develop ML-augmented spectral solvers for three common PDEs of fluid dynamics. Our models are more accurate (2-4x) than standard spectral solvers at the same resolution but have longer overall runtimes (~2x), due to the additional runtime cost of the neural network component. We also demonstrate a handful of key design principles for combining machine learning and numerical methods for solving PDEs.

Shanqing Cai, Subhashini Venugopalan, Katrin Tomanek et al.

Motivated by the need for accelerating text entry in augmentative and alternative communication (AAC) for people with severe motor impairments, we propose a paradigm in which phrases are abbreviated aggressively as primarily word-initial letters. Our approach is to expand the abbreviations into full-phrase options by leveraging conversation context with the power of pretrained large language models (LLMs). Through zero-shot, few-shot, and fine-tuning experiments on four public conversation datasets, we show that for replies to the initial turn of a dialog, an LLM with 64B parameters is able to exactly expand over 70% of phrases with abbreviation length up to 10, leading to an effective keystroke saving rate of up to about 77% on these exact expansions. Including a small amount of context in the form of a single conversation turn more than doubles abbreviation expansion accuracies compared to having no context, an effect that is more pronounced for longer phrases. Additionally, the robustness of models against typo noise can be enhanced through fine-tuning on noisy data.

Dmitrii Kochkov, Janni Yuval, Ian Langmore et al.

General circulation models (GCMs) are the foundation of weather and climate prediction. GCMs are physics-based simulators which combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine learning (ML) models trained on reanalysis data achieved comparable or better skill than GCMs for deterministic weather forecasting. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present the first GCM that combines a differentiable solver for atmospheric dynamics with ML components, and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best ML and physics-based methods. NeuralGCM is competitive with ML models for 1-10 day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for 1-15 day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics such as global mean temperature for multiple decades, and climate forecasts with 140 km resolution exhibit 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. 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.

David P. Woodruff, Vincent Cohen-Addad, Lalit Jain et al.

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

Haoyu Guo, Maria Tikhanovskaya, Paul Raccuglia et al.

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.

Qian-Ze Zhu, Paul Raccuglia, Michael P. Brenner

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.

Nayantara Mudur, Hao Cui, Subhashini Venugopalan et al.

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

Ramya Deshpande, Francesco Mottes, Ariana-Dalia Vlad et al.

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.

Sarah Martinson, Michael P. Brenner, Martyna Plomecka et al.

Probabilistic forecasting of infectious diseases is crucial for public health but relies on labor-intensive manual model curation by expert modeling teams. This bespoke development bottlenecks scalability to granular geographic resolutions or emerging pathogens. Here, we present an autonomous system using Large Language Model (LLM)-guided tree search to iteratively generate, evaluate, and optimize executable forecasting software. In a fully prospective, real-time evaluation during the 2025-2026 US respiratory season, the system autonomously discovered methodologically diverse models for influenza, COVID-19, and respiratory syncytial virus (RSV). Aggregating these machine-generated models yielded an ensemble that consistently matched or outperformed the gold-standard, human-curated Centers for Disease Control and Prevention (CDC) hub ensembles out-of-sample. The system successfully navigated data-scarce "cold start" scenarios for RSV. Moreover, controlled retrospective ablations revealed that optimizing log-scale distance metrics prevents reward hacking, while an automated judge-in-the-loop ensures structural fidelity to complex scientific theories. By autonomously translating epidemiological theory into accurate, transparent code, this framework overcomes the modeling labor bottleneck, enabling rapid deployment of expert-level disease forecasting at unprecedented scales.

Michael P. Brenner, Lizzie Dorfman, John C. Platt

We present a case study for how AI coding systems can be used to generate novel scientific hypotheses. We combine a generic coding agent (Google's AntiGravity) with an LLM-driven tree search algorithm (Empirical Research Assistance / ERA) to autonomously generate high-efficiency three-dimensional photovoltaic (3DPV) structures that overcome losses limiting flat solar panels at mid-latitudes. These structures operate by presenting favorable angles to the sun throughout the day, and for illustrative purposes we focus on optimizing performance for a single solar day. Our workflow begins by using AntiGravity to reproduce calculations \cite{bernardi2012solar} showing that 3DPV can have energy densities much higher than stationary flat PV panels. We use these initial designs as the starting point for large scale tree search, where we seek improved solutions and score them for their diurnal yield. The initial tree search leads to nominally more efficient solutions, yet they are caused by algorithmic reward hacking, arising from non-physical design features such as structurally levitating disconnected tiers and exploitations of the discretizations in the optics solver. To counteract this, we develop a workflow where the coding agent iteratively patches the physics engine with constraints to eliminate reward hacking. With reward-hacking eliminated, ERA discovers a series of designs with various constraints and improved performance, including optimal designs with different fixed collector areas, optimizing zenith tracking and avoiding self shadowing. Combining coding agents with tree search (ERA) provides a powerful platform for scientific discovery, for problems whose solutions can be empirically evaluated with a score function.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Jingxuan Fan, Sarah Martinson, Erik Y. Wang et al.

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.

Haining Pan, Nayantara Mudur, Will Taranto et al.

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.

Eser Aygün, Anastasiya Belyaeva, Gheorghe Comanici et al.

The cycle of scientific discovery is frequently bottlenecked by the slow, manual creation of software to support computational experiments. To address this, we present an AI system that creates expert-level scientific software whose goal is to maximize a quality metric. The system uses a Large Language Model (LLM) and Tree Search (TS) to systematically improve the quality metric and intelligently navigate the large space of possible solutions. The system achieves expert-level results when it explores and integrates complex research ideas from external sources. The effectiveness of tree search is demonstrated across a wide range of benchmarks. In bioinformatics, it discovered 40 novel methods for single-cell data analysis that outperformed the top human-developed methods on a public leaderboard. In epidemiology, it generated 14 models that outperformed the CDC ensemble and all other individual models for forecasting COVID-19 hospitalizations. Our method also produced state-of-the-art software for geospatial analysis, neural activity prediction in zebrafish, time series forecasting and numerical solution of integrals. By devising and implementing novel solutions to diverse tasks, the system represents a significant step towards accelerating scientific progress.

Michael P. Brenner, Vincent Cohen-Addad, David Woodruff

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral $I(N,α)$ for arbitrary loop geometries, directly improving upon recent AI-assisted attempts \cite{BCE+25} that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials $C_l^{(3/2)}$ to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for $I(N,α)$ at large $N$ that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.

Daniel J. Liebling, Malcolm Kane, Madeleine Grunde-Mclaughlin et al.

We present components of an AI-assisted academic writing system including citation recommendation and introduction writing. The system recommends citations by considering the user's current document context to provide relevant suggestions. It generates introductions in a structured fashion, situating the contributions of the research relative to prior work. We demonstrate the effectiveness of the components through quantitative evaluations. Finally, the paper presents qualitative research exploring how researchers incorporate citations into their writing workflows. Our findings indicate that there is demand for precise AI-assisted writing systems and simple, effective methods for meeting those needs.

Nicole N Khatibi, Daniil A. Radamovich, Michael P. Brenner

Recent breakthroughs have spurred claims that large language models (LLMs) match gold medal Olympiad to graduate level proficiency on mathematics benchmarks. In this work, we examine these claims in detail and assess the extent to which current benchmarks capture genuine LLM mathematical reasoning. The composition of these benchmarks, primarily drawing from the International Mathematics Olympiad (IMO) and related competitions, may overstate models reasoning ability due to potential data contamination and a narrow focus on familiar problem types. To enable a more holistic assessment of mathematical understanding, we introduce EEFSUVA, a novel benchmark curated from under circulated regional and national Olympiads of Eastern Europe and the countries from the former Soviet Union. These contests feature problems of comparable difficulty to the IMO and are renowned for demanding nonstandard problem-solving techniques, yet their problems are far less prevalent in online corpora. Preliminary results suggest that even state-of-the-art LLMs exhibit a notable performance decline on EEFSUVA relative to other Olympiad-style benchmarks. These findings also suggest the potential importance of broader evaluation datasets for a fuller assessment of mathematical reasoning and for guiding future model development.

James V. Roggeveen, Erik Y. Wang, Will Flintoft et al.

Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present HARDMath2, a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students' understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.

James V. Roggeveen, Michael P. Brenner

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true domain. We find the coefficients of the basis expansion by solving an optimization problem whereby both the equations, the boundary conditions and any optimization targets are enforced by a loss function, building on a key idea from Physics-Informed Neural Networks (PINNs). Since the representation of the function natively has exponential convergence, so does the solution of the optimization problem, as long as it can be solved efficiently. We find empirically that the optimization protocols developed for machine learning find solutions with exponential convergence on a wide range of equations. The method naturally allows for the incorporation of data assimilation by including additional terms in the loss function, and for the efficient solution of optimization problems over the PDE solutions.

Haining Pan, James V. Roggeveen, Erez Berg et al.

Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50 problems covering condensed matter theory (CMT) at the level of an expert researcher. Topics span analytical and computational approaches in quantum many-body, and classical statistical mechanics. The dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine problems they would want a research assistant to solve, including Hartree-Fock, exact diagonalization, quantum/variational Monte Carlo, density matrix renormalization group (DMRG), quantum/classical statistical mechanics, and model building. We evaluate LLMs by programmatically checking solutions against expert-supplied ground truth. We developed machine-grading, including symbolic handling of non-commuting operators via normal ordering. They generalize across tasks too. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. The best model, GPT5, solves 30\% of the problems; average across 17 models (GPT, Gemini, Claude, DeepSeek, Llama) is 11.4$\pm$2.1\%. Moreover, 18 problems are solved by none of the 17 models, and 26 by at most one. These unsolved problems span Quantum Monte Carlo, Variational Monte Carlo, and DMRG. Answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe this benchmark will guide development toward capable AI research assistants and tutors.

Katy Blumer, Subhashini Venugopalan, Michael P. Brenner et al.

We analyze a dataset of retinal images using linear probes: linear regression models trained on some "target" task, using embeddings from a deep convolutional (CNN) model trained on some "source" task as input. We use this method across all possible pairings of 93 tasks in the UK Biobank dataset of retinal images, leading to ~164k different models. We analyze the performance of these linear probes by source and target task and by layer depth. We observe that representations from the middle layers of the network are more generalizable. We find that some target tasks are easily predicted irrespective of the source task, and that some other target tasks are more accurately predicted from correlated source tasks than from embeddings trained on the same task.

Subhashini Venugopalan, Joel Shor, Manoj Plakal et al.

Automatic classification of disordered speech can provide an objective tool for identifying the presence and severity of speech impairment. Classification approaches can also help identify hard-to-recognize speech samples to teach ASR systems about the variable manifestations of impaired speech. Here, we develop and compare different deep learning techniques to classify the intelligibility of disordered speech on selected phrases. We collected samples from a diverse set of 661 speakers with a variety of self-reported disorders speaking 29 words or phrases, which were rated by speech-language pathologists for their overall intelligibility using a five-point Likert scale. We then evaluated classifiers developed using 3 approaches: (1) a convolutional neural network (CNN) trained for the task, (2) classifiers trained on non-semantic speech representations from CNNs that used an unsupervised objective [1], and (3) classifiers trained on the acoustic (encoder) embeddings from an ASR system trained on typical speech [2]. We found that the ASR encoder's embeddings considerably outperform the other two on detecting and classifying disordered speech. Further analysis shows that the ASR embeddings cluster speech by the spoken phrase, while the non-semantic embeddings cluster speech by speaker. Also, longer phrases are more indicative of intelligibility deficits than single words.

Thomas Frerix, Dmitrii Kochkov, Jamie A. Smith et al.

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems.

Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva et al.

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large eddy simulation, our results are as accurate as baseline solvers with 8-10x finer resolution in each spatial dimension, resulting in 40-80x fold computational speedups. Our method remains stable during long simulations, and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black box machine learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.

Kevin McCloskey, Ankur Taly, Federico Monti et al.

Deep neural networks have achieved state of the art accuracy at classifying molecules with respect to whether they bind to specific protein targets. A key breakthrough would occur if these models could reveal the fragment pharmacophores that are causally involved in binding. Extracting chemical details of binding from the networks could potentially lead to scientific discoveries about the mechanisms of drug actions. But doing so requires shining light into the black box that is the trained neural network model, a task that has proved difficult across many domains. Here we show how the binding mechanism learned by deep neural network models can be interrogated, using a recently described attribution method. We first work with carefully constructed synthetic datasets, in which the 'fragment logic' of binding is fully known. We find that networks that achieve perfect accuracy on held out test datasets still learn spurious correlations due to biases in the datasets, and we are able to exploit this non-robustness to construct adversarial examples that fool the model. The dataset bias makes these models unreliable for accurately revealing information about the mechanisms of protein-ligand binding. In light of our findings, we prescribe a test that checks for dataset bias given a hypothesis. If the test fails, it indicates that either the model must be simplified or regularized and/or that the training dataset requires augmentation.