Events & Conferences
Physics-constrained machine learning for scientific computing
Commercial applications of deep learning have been making headlines for years — never more so than this spring. More surprisingly, deep-learning methods have also shown promise for scientific computing, where they can be used to predict solutions to partial differential equations (PDEs). These equations are often prohibitively expensive to solve numerically; using data-driven methods has the potential to transform both scientific and engineering applications of scientific computing, including aerodynamics, ocean and climate, and reservoir modeling.
A fundamental challenge is that the predictions of deep-learning models trained on physical data typically ignore fundamental physical principles. Such models might, for instance, violate system conservation laws: the solution to a heat transfer problem may fail to conserve energy, or the solution to a fluid flow problem may fail to conserve mass. Similarly, a model’s solution may violate boundary conditions — say, allowing heat flow through an insulator at the boundary of a physical system. This can happen even when the model’s training data includes no such violations: at inference time, the model may simply extrapolate from patterns in the training data in an illicit way.
In a pair of recent papers accepted at the International Conference on Machine Learning (ICML) and the International Conference on Learning Representations (ICLR), we investigate the problems of adding known physics constraints to the predictive outputs of machine learning (ML) models when computing the solutions to PDEs.
The ICML paper, “Learning physical models that can respect conservation laws”, which we will present in July, focuses on satisfying conservation laws with black-box models. We show that, for certain types of challenging PDE problems with propagating discontinuities, known as shocks, our approach to constraining model outputs works better than its predecessors: it more sharply and accurately captures the physical solution and its uncertainty and yields better performance on downstream tasks.
In this paper, we collaborated with Derek Hansen, a PhD student in the Department of Statistics at the University of Michigan, who was an intern at AWS AI Labs at the time, and Michael Mahoney, an Amazon Scholar in Amazon’s Supply Chain Optimization Technologies organization and a professor of statistics at the University of California, Berkeley.
In a complementary paper we presented at this year’s ICLR, “Guiding continuous operator learning through physics-based boundary constraints”, we, together with Nadim Saad, an AWS AI Labs intern at the time and a PhD student at the Institute for Computational and Mathematical Engineering (ICME) at Stanford University, focus on enforcing physics through boundary conditions. The modeling approach we describe in this paper is a so-called constrained neural operator, and it exhibits up to a 20-fold performance improvement over previous operator models.
So that scientists working with models of physical systems can benefit from our work, we’ve released the code for the models described in both papers (conservation laws | boundary constraints) on GitHub. We also presented on both works in March 2023 at AAAI’s symposium on Computational Approaches to Scientific Discovery.
Danielle Maddix Robinson on physics-constrained machine learning for scientific computing
A talk presented in April 2023 at the Machine Learning and Dynamical Systems Seminar at the Alan Turing Institute.
Conservation laws
Recent work in scientific machine learning (SciML) has focused on incorporating physical constraints into the learning process as part of the loss function. In other words, the physical information is treated as a soft constraint or regularization.
A main issue with these approaches is that they do not guarantee that the physical property of conservation is satisfied. To address this issue, in “Learning physical models that can respect conservation laws”, we propose ProbConserv, a framework for incorporating constraints into a generic SciML architecture. Instead of expressing conservation laws in the differential forms of PDEs, which are commonly used in SciML as extra terms in the loss function, ProbConserv converts them into their integral form. This allows us to use ideas from finite-volume methods to enforce conservation.
In finite-volume methods, a spatial domain — say, the region through which heat is propagating — is discretized into a finite set of smaller volumes called control volumes. The method maintains the balance of mass, energy, and momentum throughout this domain by applying the integral form of the conservation law locally across each control volume. Local conservation requires that the out-flux from one volume equals the in-flux to an adjacent volume. By enforcing the conservation law across each control volume, the finite-volume method guarantees global conservation across the whole domain, where the rate of change of the system’s total mass is given by the change in fluxes along the domain boundaries.
More specifically, the first step in the ProbConserv method is to use a probabilistic machine learning model — such as a Gaussian process, attentive neural process (ANP), or ensembles of neural-network models — to estimate the mean and variance of the outputs of the physical model. We then use the integral form of the conservation law to perform a Bayesian update to the mean and covariance of the distribution of the solution profile such that it satisfies the conservation constraint exactly in the limit.
In the paper, we provide a detailed analysis of ProbConserv’s application to the generalized porous-medium equation (GPME), a widely used parameterized family of PDEs. The GPME has been used in applications ranging from underground flow transport to nonlinear heat transfer to water desalination and beyond. By varying the PDE parameters, we can describe PDE problems with different levels of complexity, ranging from “easy” problems, such as parabolic PDEs that model smooth diffusion processes, to “hard” nonlinear hyperbolic-like PDEs with shocks, such as the Stefan problem, which has been used to model two-phase flow between water and ice, crystal growth, and more complex porous media such as foams.
For easy GPME variants, ProbConserv compares well to state-of-the-art competitors, and for harder GPME variants, it outperforms other ML-based approaches that do not guarantee volume conservation. ProbConserv seamlessly enforces physical conservation constraints, maintains probabilistic uncertainty quantification (UQ), and deals well with the problem of estimating shock propagation, which is difficult given ML models’ bias toward smooth and continuous behavior. It also effectively handles heteroskedasticity, or fluctuation in variables’ standard deviations. In all cases, it achieves superior predictive performance on downstream tasks, such as predicting shock location, which is a challenging problem even for advanced numerical solvers.
Examples
Boundary conditions
Boundary conditions (BCs) are physics-enforced constraints that solutions of PDEs must satisfy at specific spatial locations. These constraints carry important physical meaning and guarantee the existence and the uniqueness of PDE solutions. Current deep-learning-based approaches that aim to solve PDEs rely heavily on training data to help models learn BCs implicitly. There is no guarantee, though, that these models will satisfy the BCs during evaluation. In our ICLR 2023 paper, “Guiding continuous operator learning through physics-based boundary constraints”, we propose an efficient, hard-constrained, neural-operator-based approach to enforcing BCs.
Where most SciML methods (for example, PINNs) parameterize the solution to PDEs with a neural network, neural operators aim to learn the mapping from PDE coefficients or initial conditions to solutions. At the core of every neural operator is a kernel function, formulated as an integral operator, that describes the evolution of a physical system over time. For our study, we chose the Fourier neural operator (FNO) as an example of a kernel-based neural operator.
We propose a model we call the boundary-enforcing operator network (BOON). Given a neural operator representing a PDE solution, a training dataset, and prescribed BCs, BOON applies structural corrections to the neural operator to ensure that the predicted solution satisfies the system BCs.
We provide our refinement procedure and demonstrate that BOON’s solutions satisfy physics-based BCs, such as Dirichlet, Neumann, and periodic. We also report extensive numerical experiments on a wide range of problems including the heat and wave equations and Burgers’s equation, along with the challenging 2-D incompressible Navier-Stokes equations, which are used in climate and ocean modeling. We show that enforcing these physical constraints results in zero boundary error and improves the accuracy of solutions on the interior of the domain. BOON’s correction method exhibits a 2-fold to 20-fold improvement over a given neural-operator model in relative L2 error.
Examples
Navier-Stokes lid-driven flow
2-D Navier-Stokes lid-driven cavity flow vorticity field. The vorticity field (perpendicular to the screen) within a square cavity filled with an incompressible fluid, which is induced by a fixed nonzero horizontal velocity prescribed by the Dirichlet boundary condition at the top boundary line for a 25-step (T=25) prediction until final time t = 2.
2-D Navier-Stokes lid-driven cavity flow relative error.
The L2 relative-error plots show significantly higher relative error over time for the data-driven Fourier neural operator (FNO) compared to that of our constrained BOON model on the Navier-Stokes lid-driven cavity flow problem for both a random test sample and the average over the test samples.
Acknowledgements: This work would have not been possible without the help of our coauthor Michael W. Mahoney, an Amazon Scholar; coauthors and PhD student interns Derek Hansen and Nadim Saad; and mentors Yuyang Wang and Margot Gerritsen.
Have you ever worked is legacy code? Are you curious what it takes to modernize systems at a massive scale?
Pascal Hartig is joined on the latest Meta Tech Podcast by Elaine and Buping, two software engineers working on a bold project to rewrite the decades-old C code in one of Meta’s core messaging libraries in Rust. It’s an ambitious effort that will transform a central messaging library that is shared across Messenger, Facebook, Instagram, and Meta’s AR/VR platforms.
They discuss taking on a project of this scope – even without a background in Rust, how they’re approaching it, and what it means to optimize for ‘developer happiness.’
Download or listen to the episode below:
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The Meta Tech Podcast is a podcast, brought to you by Meta, where we highlight the work Meta’s engineers are doing at every level – from low-level frameworks to end-user features.
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Amazon Research Awards (ARA) provides unrestricted funds and AWS Promotional Credits to academic researchers investigating various research topics in multiple disciplines. This cycle, ARA received many excellent research proposals from across the world and today is publicly announcing 73 award recipients who represent 46 universities in 10 countries.
This announcement includes awards funded under five call for proposals during the fall 2024 cycle: AI for Information Security, Automated Reasoning, AWS AI, AWS Cryptography, and Sustainability. Proposals were reviewed for the quality of their scientific content and their potential to impact both the research community and society. Additionally, Amazon encourages the publication of research results, presentations of research at Amazon offices worldwide, and the release of related code under open-source licenses.
Recipients have access to more than 700 Amazon public datasets and can utilize AWS AI/ML services and tools through their AWS Promotional Credits. Recipients also are assigned an Amazon research contact who offers consultation and advice, along with opportunities to participate in Amazon events and training sessions.
“Automated Reasoning is an important area of research for Amazon, with potential applications across various features and applications to help improve security, reliability, and performance for our customers. Through the ARA program, we collaborate with leading academic researchers to explore challenges in this field,” said Robert Jones, senior principal scientist with the Cloud Automated Reasoning Group. “We were again impressed by the exceptional response to our Automated Reasoning call for proposals this year, receiving numerous high-quality submissions. Congratulations to the recipients! We’re excited to support their work and partner with them as they develop new science and technology in this important area.”
“At Amazon, we believe that solving the world’s toughest sustainability challenges benefits from both breakthrough scientific research and open and bold collaboration. Through programs like the Amazon Research Awards program, we aim to support academic research that could contribute to our understanding of these complex issues,” said Kommy Weldemariam, Director of Science and Innovation Sustainability. “The selected proposals represent innovative projects that we hope will help advance knowledge in this field, potentially benefiting customers, communities, and the environment.”
ARA funds proposals throughout the year in a variety of research areas. Applicants are encouraged to visit the ARA call for proposals page for more information or send an email to be notified of future open calls.
The tables below list, in alphabetical order by last name, fall 2024 cycle call-for-proposal recipients, sorted by research area.
AI for Information Security
| Recipient | University | Research title |
| Christopher Amato | Northeastern University | Multi-Agent Reinforcement Learning Cyber Defense for Securing Cloud Computing Platforms |
| Bernd Bischl | Ludwig Maximilian University of Munich | Improving Generative and Foundation Models Reliability via Uncertainty-awareness |
| Shiqing Ma | University Of Massachusetts Amherst | LLM and Domain Adaptation for Attack Detection |
| Alina Oprea | Northeastern University | Multi-Agent Reinforcement Learning Cyber Defense for Securing Cloud Computing Platforms |
| Roberto Perdisci | University of Georgia | ContextADBench: A Comprehensive Benchmark Suite for Contextual Anomaly Detection |
Automated Reasoning
| Recipient | University | Research title |
| Nada Amin | Harvard University | LLM-Augmented Semi-Automated Proofs for Interactive Verification |
| Suguman Bansal | Georgia Institute of Technology | Certified Inductive Generalization in Reinforcement Learning |
| Ioana Boureanu | University of Surrey | Phoebe+: An Automated-Reasoning Tool for Provable Privacy in Cryptographic Systems |
| Omar Haider Chowdhury | Stony Brook University | Restricter: An Automatic Tool for Authoring Amazon Cedar Access Control Policies with the Principle of Least Privilege |
| Stefan Ciobaca | Alexandru Ioan Cuza University | An Interactive Proof Mode for Dafny |
| João Ferreira | INESC-ID | Polyglot Automated Program Repair for Infrastructure as Code |
| Sicun Gao | University Of California, San Diego | Monte Carlo Trees with Conflict Models for Proof Search |
| Mirco Giacobbe | University of Birmingham | Neural Software Verification |
| Tobias Grosser | University of Cambridge | Synthesis-based Symbolic BitVector Simplification for Lean |
| Ronghui Gu | Columbia University | Scaling Formal Verification of Security Properties for Unmodified System Software |
| Alexey Ignatiev | Monash University | Huub: Next-Gen Lazy Clause Generation |
| Kenneth McMillan | University of Texas At Austin | Synthesis of Auxiliary Variables and Invariants for Distributed Protocol Verification |
| Alexandra Mendes | University of Porto | Overcoming Barriers to the Adoption of Verification-Aware Languages |
| Jason Nieh | Columbia University | Scaling Formal Verification of Security Properties for Unmodified System Software |
| Rohan Padhye | Carnegie Mellon University | Automated Synthesis and Evaluation of Property-Based Tests |
| Nadia Polikarpova | University Of California, San Diego | Discovering and Proving Critical System Properties with LLMs |
| Fortunat Rajaona | University of Surrey | Phoebe+: An Automated-Reasoning Tool for Provable Privacy in Cryptographic Systems |
| Subhajit Roy | Indian Institute of Technology Kanpur | Theorem Proving Modulo LLM |
| Gagandeep Singh | University of Illinois At Urbana–Champaign | Trustworthy LLM Systems using Formal Contracts |
| Scott Stoller | Stony Brook University | Restricter: An Automatic Tool for Authoring Amazon Cedar Access Control Policies with the Principle of Least Privilege |
| Peter Stuckey | Monash University | Huub: Next-Gen Lazy Clause Generation |
| Yulei Sui | University of New South Wales | Path-Sensitive Typestate Analysis through Sparse Abstract Execution |
| Nikos Vasilakis | Brown University | Semantics-Driven Static Analysis for the Unix/Linux Shell |
| Ping Wang | Stevens Institute of Technology | Leveraging Large Language Models for Reasoning Augmented Searching on Domain-specific NoSQL Database |
| John Wawrzynek | University of California, Berkeley | GPU-Accelerated High-Throughput SAT Sampling |
AWS AI
| Recipient | University | Research title |
| Panagiotis Adamopoulos | Emory University | Generative AI solutions for The Spillover Effect of Fraudulent Reviews on Product Recommendations |
| Vikram Adve | University of Illinois at Urbana–Champaign | Fellini: Differentiable ML Compiler for Full-Graph Optimization for LLM Models |
| Frances Arnold | California Institute of Technology | Closed-loop Generative Machine Learning for De Novo Enzyme Discovery and Optimization |
| Yonatan Bisk | Carnegie Mellon University | Useful, Safe, and Robust Multiturn Interactions with LLMs |
| Shiyu Chang | University of California, Santa Barbara | Cut the Crap: Advancing the Efficient Communication of Multi-Agent Systems via Spatial-Temporal Topology Design and KV Cache Sharing |
| Yuxin Chen | University of Pennsylvania | Provable Acceleration of Diffusion Models for Modern Generative AI |
| Tianlong Chen | University of North Carolina at Chapel Hill | Cut the Crap: Advancing the Efficient Communication of Multi-Agent Systems via Spatial-Temporal Topology Design and KV Cache Sharing |
| Mingyu Ding | University of North Carolina at Chapel Hill | Aligning Long Videos and Language as Long-Horizon World Models |
| Nikhil Garg | Cornell University | Market Design for Responsible Multi-agent LLMs |
| Jessica Hullman | Northwestern University | Human-Aligned Uncertainty Quantification in High Dimensions |
| Christopher Jermaine | Rice University | Fast, Trusted AI Using the EINSUMMABLE Compiler |
| Yunzhu Li | Columbia University | Physics-Informed Foundation Models Through Embodied Interactions |
| Pattie Maes | Massachusetts Institute of Technology | Understanding How LLM Agents Deviate from Human Choices |
| Sasa Misailovic | University of Illinois at Urbana–Champaign | Fellini: Differentiable ML Compiler for Full-Graph Optimization for LLM Models |
| Kristina Monakhova | Cornell University | Trustworthy extreme imaging for science using interpretable uncertainty quantification |
| Todd Mowry | Carnegie Mellon University | Efficient LLM Serving on Trainium via Kernel Generation |
| Min-hwan Oh | Seoul National University | Mutually Beneficial Interplay Between Selection Fairness and Context Diversity in Contextual Bandits |
| Patrick Rebeschini | University of Oxford | Optimal Regularization for LLM Alignment |
| Jose Renau | University of California, Santa Cruz | Verification Constrained Hardware Optimization using Intelligent Design Agentic Programming |
| Vilma Todri | Emory University | Generative AI solutions for The Spillover Effect of Fraudulent Reviews on Product Recommendations |
| Aravindan Vijayaraghavan | Northwestern University | Human-Aligned Uncertainty Quantification in High Dimensions |
| Wei Yang | University of Texas at Dallas | Optimizing RISC-V Compilers with RISC-LLM and Syntax Parsing |
| Huaxiu Yao | University of North Carolina at Chapel Hill | Aligning Long Videos and Language as Long-Horizon World Models |
| Amy Zhang | University of Washington | Tools for Governing AI Agent Autonomy |
| Ruqi Zhang | Purdue University | Efficient Test-time Alignment for Large Language Models and Large Multimodal Models |
| Zheng Zhang | Rutgers University-New Brunswick | AlphaQC: An AI-powered Quantum Circuit Optimizer and Denoiser |
AWS Cryptography
| Recipient | University | Research title |
| Alexandra Boldyreva | Georgia Institute of Technology | Quantifying Information Leakage in Searchable Encryption Protocols |
| Maria Eichlseder | Graz University of Technology, Austria | SALAD – Systematic Analysis of Lightweight Ascon-based Designs |
| Venkatesan Guruswami | University of California, Berkeley | Obfuscation, Proof Systems, and Secure Computation: A Research Program on Cryptography at the Simons Institute for the Theory of Computing |
| Joseph Jaeger | Georgia Institute of Technology | Analyzing Chat Encryption for Group Messaging |
| Aayush Jain | Carnegie Mellon | Large Scale Multiparty Silent Preprocessing for MPC from LPN |
| Huijia Lin | University of Washington | Large Scale Multiparty Silent Preprocessing for MPC from LPN |
| Hamed Nemati | KTH Royal Institute of Technology | Trustworthy Automatic Verification of Side-Channel Countermeasures for Binary Cryptographic Programs using the HoIBA libary |
| Karl Palmskog | KTH Royal Institute of Technology | Trustworthy Automatic Verification of Side-Channel Countermeasures for Binary Cryptographic Programs using the HoIBA libary |
| Chris Peikert | University of Michigan, Ann Arbor | Practical Third-Generation FHE and Bootstrapping |
| Dimitrios Skarlatos | Carnegie Mellon University | Scale-Out FHE LLMs on GPUs |
| Vinod Vaikuntanathan | Massachusetts Institute of Technology | Can Quantum Computers (Really) Factor? |
| Daniel Wichs | Northeastern University | Obfuscation, Proof Systems, and Secure Computation: A Research Program on Cryptography at the Simons Institute for the Theory of Computing |
| David Wu | University Of Texas At Austin | Fast Private Information Retrieval and More using Homomorphic Encryption |
Sustainability
| Recipient | University | Research title |
| Meeyoung Cha | Max Planck Institute | Forest-Blossom (Flossom): A New Framework for Sustaining Forest Biodiversity Through Outcome-Driven Remote Sensing Monitoring |
| Jingrui He | University of Illinois at Urbana–Champaign | Foundation Model Enabled Earth’s Ecosystem Monitoring |
| Pedro Lopes | University of Chicago | AI-powered Tools that Enable Engineers to Make & Re-make Sustainable Hardware |
| Cheng Yaw Low | Max Planck Institute | Forest-Blossom (Flossom): A New Framework for Sustaining Forest Biodiversity Through Outcome-Driven Remote Sensing Monitoring |
AI safety is a priority at Amazon. Our investment in safe, transparent, and responsible AI (RAI) includes collaboration with the global community and policymakers. We are members of and collaborate with organizations such as the Frontier Model Forum, the Partnership on AI, and other forums organized by government agencies such as the National Institute of Standards and Technology (NIST). Consistent with Amazon’s endorsement of the Korea Frontier AI Safety Commitments, we published our Frontier Model Safety Framework earlier this year.
During the development of the Nova Premier model, we conducted a comprehensive evaluation to assess its performance and safety. This included testing on both internal and public benchmarks and internal/automated and third-party red-teaming exercises. Once the final model was ready, we prioritized obtaining unbiased, third-party evaluations of the model’s robustness against RAI controls. In this post, we outline the key findings from these evaluations, demonstrating the strength of our testing approach and Amazon Premier’s standing as a safe model. Specifically, we cover our evaluations with two third-party evaluators: PRISM AI and ActiveFence.
Evaluation of Nova Premier against PRISM AI
PRISM Eval’s Behavior Elicitation Tool (BET) dynamically and systematically stress-tests AI models’ safety guardrails. The methodology focuses on measuring how many adversarial attempts (steps) it takes to get a model to generate harmful content across several key risk dimensions. The central metric is “steps to elicit” — the number of increasingly sophisticated prompting attempts required before a model generates an inappropriate response. A higher number of steps indicates stronger safety measures, as the model is more resistant to manipulation. The PRISM risk dimensions (inspired by the MLCommons AI Safety Benchmarks) include CBRNE weapons, violent crimes, non-violent crimes, defamation, and hate, amongst several others.
Using the BET Eval tool and its V1.0 metric, which is tailored toward non-reasoning models, we compared the recently released Nova models (Pro and Premier) to the latest models in the same class: Claude (3.5 v2 and 3.7 non-reasoning) and Llama4 Maverick, all available through Amazon Bedrock. PRISM BET conducts black-box evaluations (where model developers don’t have access to the test prompts) of models integrated with their API. The evaluation conducted with BET Eval MAX, PRISM’s most comprehensive/aggressive testing suite, revealed significant variations in safety against malicious instructions. Nova models demonstrated superior overall safety performance, with an average of 43 steps for Premier and 52 steps for Pro, compared to 37.7 for Claude 3.5 v2 and fewer than 12 steps for other models in the comparison set (namely, 9.9 for Claude3.7, 11.5 for Claude 3.7 thinking, and 6.5 for Maverick). This higher step count suggests that on average, Nova’s safety guardrails are more sophisticated and harder to circumvent through adversarial prompting. The figure below presents the number of steps per harm category evaluated through BET Eval MAX.
The PRISM evaluation provides valuable insights into the relative safety of different Amazon Bedrock models. Nova’s strong performance, particularly in hate speech and defamation resistance, represents meaningful progress in AI safety. However, the results also highlight the ongoing challenge of building truly robust safety measures into AI systems. As the field continues to evolve, frameworks like BET will play an increasingly important role in benchmarking and improving AI safety. As a part of this collaboration Nicolas Miailhe, CEO of PRISM Eval, said, “It’s incredibly rewarding for us to see Nova outperforming strong baselines using the BET Eval MAX; our aim is to build a long-term partnership toward safer-by-design models and to make BET available to various model providers.” Organizations deploying AI systems should carefully consider these safety metrics when selecting models for their applications.
Manual red teaming with ActiveFence
The AI safety & security company ActiveFence benchmarked Nova Premier on Bedrock on prompts distributed across Amazon’s eight core RAI categories. ActiveFence also evaluated Claude 3.7 (non-reasoning mode) and GPT 4.1 API on the same set. The flag rate on Nova Premier was lower than that on the other two models, indicating that Nova Premier is the safest of the three.
| Model | 3P Flag Rate [↓ is better] |
| Nova Premier | 12.0% |
| Sonnet 3.7 (non-reasoning) | 20.6% |
| GPT4.1 API | 22.4% |
“Our role is to think like an adversary but act in service of safety,” said Guy Paltieli from ActiveFence. “By conducting a blind stress test of Nova Premier under realistic threat scenarios, we helped evaluate its security posture in support of Amazon’s broader responsible-AI goals, ensuring the model could be deployed with greater confidence.”
These evaluations conducted with PRISM and ActiveFence give us confidence in the strength of our guardrails and our ability to protect our customers’ safety when they use our models. While these evaluations demonstrate strong safety performance, we recognize that AI safety is an ongoing challenge requiring continuous improvement. These assessments represent a point-in-time snapshot, and we remain committed to regular testing and enhancement of our safety measures. No AI system can guarantee perfect safety in all scenarios, which is why we maintain monitoring and response systems after deployment.
Acknowledgments: Vincent Ponzo, Elyssa Vincent
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