Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
135 papers in Foundation models · newest first
physics.flu-dyn
Computational fluid dynamics (CFD) drives progress in numerous scientific and engineering fields, yet high-fidelity simulations remain computationally prohibitive. While machine learning approaches offer computing acceleration, they typically specialize in single physical systems or require extensive training data, hindering their applicability in highly nonlinear and 3D flow scenarios. To overcome these limitations, we propose OmniFluids, a pure physics pre-trained model that captures fundamental fluid dynamics laws and adapts efficiently to diverse downstream tasks with minimal data. We develop a training framework combining physics-only pre-training, coarse-grid operator distillation, and few-shot fine-tuning. This enables OmniFluids to retain broad physics knowledge while delivering fast and accurate predictions. Architecturally, OmniFluids integrates a mixture of operators, a multi-frame decoder, and factorized Fourier layers, seamlessly incorporating physics-based supervision while allowing efficient and scalable modeling of diverse tasks. Extensive tests on a broad range of 2D and 3D benchmarks show that OmniFluids outperforms state-of-the-art AI-driven methods in terms of flow field prediction and turbulence statistics. It delivers 10–100 speedups over traditional solvers while maintaining a comparable accuracy and accurately identifies unknown physical parameters from sparse, noisy data. This work demonstrates the potential of training a unified CFD solver exclusively from physics knowledge, offering a new approach for efficient and generalizable modeling across complex fluid systems.
cs.LG
We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations.
cs.RO
Autonomous robots must reason about the physical consequences of their actions to operate effectively in unstructured, real-world environments. We present Scan, Materialize, Simulate (SMS), a unified framework that combines 3D Gaussian Splatting for accurate scene reconstruction, visual foundation models for semantic segmentation, vision-language models for material property inference, and physics simulation for reliable prediction of action outcomes. By integrating these components, SMS enables generalizable physical reasoning and object-centric planning without the need to re-learn foundational physical dynamics. We empirically validate SMS in a billiards-inspired manipulation task and a challenging quadrotor landing scenario, demonstrating robust performance on both simulated domain transfer and real-world experiments. Our results highlight the potential of bridging differentiable rendering for scene reconstruction, foundation models for semantic understanding, and physics-based simulation to achieve physically grounded robot planning across diverse settings.
cs.LG
Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen chaotic systems preserving both short-term accuracy and distributional measures, nonlinear resonance patterns in attention heads, and effective prediction of real-world experimental time series. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We also demonstrate a neural scaling law for differential equations, underscoring the potential of pre-trained models for probing abstract mathematical domains like nonlinear dynamics.
cs.LG
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing error accumulation. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to the out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at https://github.com/SCAILab-USTC/PITA.
cs.LG
Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PDEs), enabling transfer across tasks and domains. While physics-informed methods, which leverage PDE residuals as supervisory signals, have shown promise in scientific machine learning (SciML) for improving accuracy and reducing data requirements, their potential in the context of SciFMs remains relatively unexplored. In this evaluation study, we investigate whether (and how) physics-informed pre-training improves the generalization, robustness, and data efficiency of SciFMs. We conduct systematic experiments across a diverse set of PDEs, ranging from simple problems with periodic boundary conditions to more challenging systems such as the Navier-Stokes equations and non-periodic geometries. Our results show that physics-informed pre-training provides clear benefits in ``nice,'' e.g., structured, well-aligned settings: it enhances generalization and reduces data dependence, compared to data-only pre-training. However, these advantages diminish significantly as the downstream tasks become ``harder,'' e.g., as they involve discontinuities or deviate from the pre-training distribution. In complex or structurally different problems, such as those involving new boundary conditions or PDE operators, physics-informed models may perform only on par with—or even worse—than data-driven baselines. While residual-based pre-training helps in idealized regimes, realizing broadly transferable SciFMs will likely require subtler spatiotemporal inductive biases and more principled integration of physical knowledge into model architectures.
cs.LG
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.
cs.LG
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed for single PDEs, limiting their generalizability across different physical systems. In this work, we explore the potential of a foundation PINN model capable of solving multiple PDEs within a unified architecture. We investigate the efficacy of a single PINN framework trained on four distinct PDEs-the Simple Harmonic Oscillator (SHO), the 1D Heat Equation, the 1D Wave Equation, and the 2D Laplace Equation, demonstrating its ability to learn diverse physical dynamics. To enhance sample efficiency, we incorporate Active Learning (AL) using Monte Carlo (MC) Dropout-based uncertainty estimation, selecting the most informative training samples iteratively. We evaluate different active learning strategies, comparing models trained on 10%, 20%, 30%, 40%, and 50% of the full dataset, and analyze their impact on solution accuracy. Our results indicate that targeted uncertainty sampling significantly improves performance with fewer training samples, leading to efficient learning across multiple PDEs. This work highlights the feasibility of a generalizable PINN-based foundation model, capable of adapting to different physics-based problems without redesigning network architectures. Our findings suggest that multi-PDE PINNs with active learning can serve as an effective approach for reducing computational costs while maintaining high accuracy in physics-based deep learning applications.
physics.flu-dyn
Multiphase fluid dynamics, such as falling droplets and rising bubbles, are critical to many industrial applications. However, simulating these phenomena efficiently is challenging due to the complexity of instabilities, wave patterns, and bubble breakup. This paper investigates the potential of scientific machine learning (SciML) to model these dynamics using neural operators and foundation models. We apply sequence-to-sequence techniques on a comprehensive dataset generated from 11,000 simulations, comprising 1 million time snapshots, produced with a well-validated Lattice Boltzmann method (LBM) framework. The results demonstrate the ability of machine learning models to capture transient dynamics and intricate fluid interactions, paving the way for more accurate and computationally efficient SciML-based solvers for multiphase applications.
cs.LG
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to train approximations to multiple differential equations simultaneously and are thus a general purpose solver that can be adapted to downstream tasks. Current PDE foundation models focus on either learning general solution operators and/or the governing system of equations, and thus only handle numerical or symbolic modalities. However, real-world applications may require more flexible data modalities, e.g. text analysis or descriptive outputs. To address this gap, we propose a novel multimodal deep learning approach that leverages a transformer-based architecture to approximate solution operators for a wide variety of ODEs and PDEs. Our method integrates numerical inputs, such as equation parameters and initial conditions, with text descriptions of physical processes or system dynamics. This enables our model to handle settings where symbolic representations may be incomplete or unavailable. In addition to providing accurate numerical predictions, our approach generates interpretable scientific text descriptions, offering deeper insights into the underlying dynamics and solution properties. The numerical experiments show that our model provides accurate solutions for in-distribution data (with average relative error less than 3.3%) and out-of-distribution data (average relative error less than 7.8%) together with precise text descriptions (with correct descriptions generated 100% of times). In certain tests, the model is also shown to be capable of extrapolating solutions in time.
cs.LG
Differentially private (DP) synthetic data enables the use of sensitive datasets while providing strong privacy guarantees. Recently, Private Evolution (PE) has emerged as a promising framework for generating DP synthetic data using only inference APIs of foundation models. However, suitable foundation models are not always available for every private data domain. In this paper, we show that PE is more general than previously understood and can incorporate APIs beyond foundation models. In particular, we show that state-of-the-art non-neural-network data synthesizers, including computer graphics-based image generators and physics simulation tools (which we refer to as simulators), integrate naturally into PE. We call the resulting method Sim-PE. Sim-PE broadens the applicability of PE while improving performance. For image synthesis, Sim-PE improves downstream classification accuracy by up to 3x, reduces FID by up to 80%, and is significantly more efficient. We further show that simulators and foundation models can be seamlessly combined within Sim-PE for additional gains. Beyond performance improvements, Sim-PE enables new DP applications that are difficult or impossible for existing methods, including generating DP control signals whose execution reproduces the distribution of private observations. The code is open-sourced in the Private Evolution Python library: https://github.com/microsoft/DPSDA
cs.LG
We introduce BCAT, a PDE foundation model designed for autoregressive prediction of solutions to two dimensional fluid dynamics problems. Our approach uses a block causal transformer architecture to model next frame predictions, leveraging previous frames as contextual priors rather than relying solely on sub-frames or pixel-based inputs commonly used in image generation methods. This block causal framework more effectively captures the spatial dependencies inherent in nonlinear spatiotemporal dynamics and physical phenomena. In an ablation study, next frame prediction demonstrated a 3.5x accuracy improvement over next token prediction. BCAT is trained on a diverse range of fluid dynamics datasets, including incompressible and compressible Navier-Stokes equations across various geometries and parameter regimes, as well as the shallow-water equations. The model's performance was evaluated on 6 distinct downstream prediction tasks and tested on about 8K trajectories to measure robustness on a variety of fluid dynamics simulations. BCAT achieved an average relative error of 1.18% across all evaluation tasks, outperforming prior approaches on standard benchmarks. With fine-tuning on a turbulence dataset, we show that the method adapts to new settings with more than 40% better accuracy over prior methods.
cs.LG
Meshes are used to represent complex objects in high fidelity physics simulators across a variety of domains, such as radar sensing and aerodynamics. There is growing interest in using neural networks to accelerate physics simulations, and also a growing body of work on applying neural networks directly to irregular mesh data. Since multiple mesh topologies can represent the same object, mesh augmentation is typically required to handle topological variation when training neural networks. Due to the sensitivity of physics simulators to small changes in mesh shape, it is challenging to use these augmentations when training neural network-based physics simulators. In this work, we show that variations in mesh topology can significantly reduce the performance of neural network simulators. We evaluate whether pretraining can be used to address this issue, and find that employing an established autoencoder pretraining technique with graph embedding models reduces the sensitivity of neural network simulators to variations in mesh topology. Finally, we highlight future research directions that may further reduce neural simulator sensitivity to mesh topology.
physics.flu-dyn
This work presents a large language model (LLM)-based agent OpenFOAMGPT tailored for OpenFOAM-centric computational fluid dynamics (CFD) simulations, leveraging two foundation models from OpenAI: the GPT-4o and a chain-of-thought (CoT)-enabled o1 preview model. Both agents demonstrate success across multiple tasks. While the price of token with o1 model is six times as that of GPT-4o, it consistently exhibits superior performance in handling complex tasks, from zero-shot case setup to boundary condition modifications, turbulence model adjustments, and code translation. Through an iterative correction loop, the agent efficiently addressed single- and multi-phase flow, heat transfer, RANS, LES, and other engineering scenarios, often converging in a limited number of iterations at low token costs. To embed domain-specific knowledge, we employed a retrieval-augmented generation (RAG) pipeline, demonstrating how preexisting simulation setups can further specialize the agent for sub-domains such as energy and aerospace. Despite the great performance of the agent, human oversight remains crucial for ensuring accuracy and adapting to shifting contexts. Fluctuations in model performance over time suggest the need for monitoring in mission-critical applications. Although our demonstrations focus on OpenFOAM, the adaptable nature of this framework opens the door to developing LLM-driven agents into a wide range of solvers and codes. By streamlining CFD simulations, this approach has the potential to accelerate both fundamental research and industrial engineering advancements.
cs.LG
Rapid and accurate simulations of fluid dynamics around complicated geometric bodies are critical in a variety of engineering and scientific applications, including aerodynamics and biomedical flows. However, while scientific machine learning (SciML) has shown considerable promise, most studies in this field are limited to simple geometries, and complex, real-world scenarios are underexplored. This paper addresses this gap by benchmarking diverse SciML models, including neural operators and vision transformer-based foundation models, for fluid flow prediction over intricate geometries. Using a high-fidelity dataset of steady-state flows across various geometries, we evaluate the impact of geometric representations – Signed Distance Fields (SDF) and binary masks – on model accuracy, scalability, and generalization. Central to this effort is the introduction of a novel, unified scoring framework that integrates metrics for global accuracy, boundary layer fidelity, and physical consistency to enable a robust, comparative evaluation of model performance. Our findings demonstrate that newer foundation models significantly outperform neural operators, particularly in data-limited scenarios, and that SDF representations yield superior results with sufficient training data. Despite these promises, all models struggle with out-of-distribution generalization, highlighting a critical challenge for future SciML applications. By advancing both evaluation models and modeling capabilities, our work paves the way for robust and scalable ML solutions for fluid dynamics across complex geometries.
cs.AI
Significant advances have been achieved in leveraging foundation models, such as large language models (LLMs), to accelerate complex scientific workflows. In this work we introduce FoamPilot, a proof-of-concept LLM agent designed to enhance the usability of FireFOAM, a specialized solver for fire dynamics and fire suppression simulations built using OpenFOAM, a popular open-source toolbox for computational fluid dynamics (CFD). FoamPilot provides three core functionalities: code insight, case configuration and simulation evaluation. Code insight is an alternative to traditional keyword searching leveraging retrieval-augmented generation (RAG) and aims to enable efficient navigation and summarization of the FireFOAM source code for developers and experienced users. For case configuration, the agent interprets user requests in natural language and aims to modify existing simulation setups accordingly to support intermediate users. FoamPilot's job execution functionality seeks to manage the submission and execution of simulations in high-performance computing (HPC) environments and provide preliminary analysis of simulation results to support less experienced users. Promising results were achieved for each functionality, particularly for simple tasks, and opportunities were identified for significant further improvement for more complex tasks. The integration of these functionalities into a single LLM agent is a step aimed at accelerating the simulation workflow for engineers and scientists employing FireFOAM for complex simulations critical for improving fire safety.
cs.LG
The emergence of the Large Language Model (LLM) has shown their superiority in a wide range of disciplines, including language understanding and translation, relational logic reasoning, and even partial differential equations solving. The transformer is the pervasive backbone architecture for the foundation model construction. It is vital to research how to adjust the Transformer architecture to achieve an end-to-end privacy guarantee in LLM fine-tuning. In this paper, we investigate three potential information leakage during a federated fine-tuning procedure for LLM (FedLLM). Based on the potential information leakage, we provide an end-to-end privacy guarantee solution for FedLLM by inserting two-stage randomness. The first stage is to train a gradient auto-encoder with a Gaussian random prior based on the statistical information of the gradients generated by local clients. The second stage is to fine-tune the overall LLM with a differential privacy guarantee by adopting appropriate Gaussian noises. We show the efficiency and accuracy gains of our proposed method with several foundation models and two popular evaluation benchmarks. Furthermore, we present a comprehensive privacy analysis with Gaussian Differential Privacy (GDP) and Renyi Differential Privacy (RDP).
cs.LG
Recent developments in 3D vision have enabled significant progress in inferring neural fluid fields and realistic rendering of fluid dynamics. However, these methods require dense captures of real-world flows, which demand specialized laboratory setups, making the process costly and challenging. Scientific machine learning (SciML) foundation models, pretrained on extensive simulations of partial differential equations (PDEs), encode rich multiphysics knowledge and thus provide promising sources of domain priors for fluid field inference. Nevertheless, the transferability of these foundation models to real-world vision problems remains largely underexplored. In this work, we demonstrate that SciML foundation models can significantly reduce the data requirements for inferring real-world 3D fluid dynamics while improving generalization. Our method leverages the strong forecasting capabilities and meaningful representations learned by SciML foundation models. We introduce a novel collaborative training strategy that equips neural fluid fields with augmented frames and fluid features extracted from the foundation model. Extensive experiments show substantial improvements in both quantitative metrics and visual quality over prior approaches. In particular, our method achieves a 9-36% improvement in peak signal-to-noise ratio (PSNR) for future prediction while reducing the number of required training frames by 25-50%. These results highlight the practical applicability of SciML foundation models for real-world fluid dynamics reconstruction. Our code is available at: https://github.com/delta-lab-ai/SciML-HY.
cs.LG
Differentiable Programming for scientific machine learning (SciML) has recently seen considerable interest and success, as it directly embeds neural networks inside PDEs, often called as NeuralPDEs, derived from first principle physics. Therefore, there is a widespread assumption in the community that NeuralPDEs are more trustworthy and generalizable than black box models. However, like any SciML model, differentiable programming relies predominantly on high-quality PDE simulations as "ground truth" for training. However, mathematics dictates that these are only discrete numerical approximations of the true physics. Therefore, we ask: Are NeuralPDEs and differentiable programming models trained on PDE simulations as physically interpretable as we think? In this work, we rigorously attempt to answer these questions, using established ideas from numerical analysis, experiments, and analysis of model Jacobians. Our study shows that NeuralPDEs learn the artifacts in the simulation training data arising from the discretized Taylor Series truncation error of the spatial derivatives. Additionally, NeuralPDE models are systematically biased, and their generalization capability is likely enabled by a fortuitous interplay of numerical dissipation and truncation error in the training dataset and NeuralPDE, which seldom happens in practical applications. This bias manifests aggressively even in relatively accessible 1-D equations, raising concerns about the veracity of differentiable programming on complex, high-dimensional, real-world PDEs, and in dataset integrity of foundation models. Further, we observe that the initial condition constrains the truncation error in initial-value problems in PDEs, thereby exerting limitations to extrapolation. Finally, we demonstrate that an eigenanalysis of model weights can indicate a priori if the model will be inaccurate for out-of-distribution testing.
cs.LG
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for downstream tasks. Operator learning effectively approximates solution operators for PDEs and various PDE-related problems, yet it often struggles to generalize to new tasks. To address this, we investigate fine-tuning a pretrained model, while carefully selecting an initialization that enables rapid adaptation to new tasks with minimal data. Our approach combines distributed learning to integrate data from various operators in pre-training, while physics-informed methods enable zero-shot fine-tuning, minimizing the reliance on downstream data. We investigate standard fine-tuning and Low-Rank Adaptation fine-tuning, applying both to train complex nonlinear target operators that are difficult to learn only using random initialization. Through comprehensive numerical examples, we demonstrate the advantages of our approach, showcasing significant improvements in accuracy. Our findings provide a robust framework for advancing multi-operator learning and highlight the potential of transfer learning techniques in this domain.