Physics-Informed Inference Time Scaling via Simulation-Calibrated Scientific Machine Learning

• URL: http://arxiv.org/abs/2504.16172v2
• Date: Fri, 25 Apr 2025 15:12:10 GMT
• Title: Physics-Informed Inference Time Scaling via Simulation-Calibrated Scientific Machine Learning
• Authors: Zexi Fan, Yan Sun, Shihao Yang, Yiping Lu,
• Abstract summary: High-dimensional partial differential equations (PDEs) pose significant computational challenges across fields ranging from quantum chemistry to economics and finance.<n>Although scientific machine learning (SciML) techniques offer approximate solutions, they often suffer from bias and neglect crucial physical insights.<n>We propose Simulation-Calibrated Scientific Machine Learning (SCa), a framework that dynamically refines and debiases the SCiML predictions during inference by enforcing the physical laws.
• Score: 5.728698570173857
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: High-dimensional partial differential equations (PDEs) pose significant computational challenges across fields ranging from quantum chemistry to economics and finance. Although scientific machine learning (SciML) techniques offer approximate solutions, they often suffer from bias and neglect crucial physical insights. Inspired by inference-time scaling strategies in language models, we propose Simulation-Calibrated Scientific Machine Learning (SCaSML), a physics-informed framework that dynamically refines and debiases the SCiML predictions during inference by enforcing the physical laws. SCaSML leverages derived new physical laws that quantifies systematic errors and employs Monte Carlo solvers based on the Feynman-Kac and Elworthy-Bismut-Li formulas to dynamically correct the prediction. Both numerical and theoretical analysis confirms enhanced convergence rates via compute-optimal inference methods. Our numerical experiments demonstrate that SCaSML reduces errors by 20-50% compared to the base surrogate model, establishing it as the first algorithm to refine approximated solutions to high-dimensional PDE during inference. Code of SCaSML is available at https://github.com/Francis-Fan-create/SCaSML.

Related papers

• EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations [0.8345452787121658]
  We propose EquiNO as a $textitcomplementary$ physics-informed PDE surrogate for predicting microscale physics.<n>Our framework, applicable to the so-called multiscale FE$,2,$ computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL)
  arXiv  Detail & Related papers  (2025-03-27T08:42:13Z)
• RoSTE: An Efficient Quantization-Aware Supervised Fine-Tuning Approach for Large Language Models [53.571195477043496]
  We propose an algorithm named Rotated Straight-Through-Estimator (RoSTE) RoSTE combines quantization-aware supervised fine-tuning (QA-SFT) with an adaptive rotation strategy to reduce activation outliers. Our findings reveal that the prediction error is directly proportional to the quantization error of the converged weights, which can be effectively managed through an optimized rotation configuration.
  arXiv  Detail & Related papers  (2025-02-13T06:44:33Z)
• Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning [3.912796219404492]
  SciML is a research field which combines physics-based and data-driven models.<n>Data-driven models aim to extract relations between input and output data.<n>We discuss the successful application of SciML to the simulation of the human cardiac function.
  arXiv  Detail & Related papers  (2025-01-30T19:09:38Z)
• Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey [51.87875066383221]
  This paper introduces fundamental concepts, traditional methods, and benchmark datasets, then examine the various roles Machine Learning plays in improving CFD. We highlight real-world applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, combustion, atmosphere & ocean science, biology fluid, plasma, symbolic regression, and reduced order modeling. We draw the conclusion that ML is poised to significantly transform CFD research by enhancing simulation accuracy, reducing computational time, and enabling more complex analyses of fluid dynamics.
  arXiv  Detail & Related papers  (2024-08-22T07:33:11Z)
• Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning [1.8175282137722093]
  Uncertainty (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying the reliability of the learned models. We provide a new interpretation for UQ problems by establishing a new theoretical connection between some Bayesian inference problems arising in SciML and viscous Hamilton-Jacobi partial differential equations (HJ PDEs) We develop a new Riccati-based methodology that provides computational advantages when continuously updating the model predictions.
  arXiv  Detail & Related papers  (2024-04-12T20:54:01Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits [70.97518416003358]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning on noisy intermediate-scale quantum (NISQ) devices. While tensor-train networks (TTNs) can enhance VQC representation and generalization, the resulting hybrid model, TTN-VQC, faces optimization challenges due to the Polyak-Lojasiewicz (PL) condition. To mitigate this challenge, we introduce Pre+TTN-VQC, a pre-trained TTN model combined with a VQC.
  arXiv  Detail & Related papers  (2023-05-18T03:08:18Z)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics [77.34726150561087]
  Recent developments in artificial neural networks, particularly deep learning (DL), are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics.
  arXiv  Detail & Related papers  (2022-12-18T02:03:00Z)
• Hessian-based toolbox for reliable and interpretable machine learning in physics [58.720142291102135]
  We present a toolbox for interpretability and reliability, extrapolation of the model architecture. It provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an agnostic score for the model predictions. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.
  arXiv  Detail & Related papers  (2021-08-04T16:32:59Z)
• Recurrent Localization Networks applied to the Lippmann-Schwinger Equation [0.0]
  We present a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains.
  arXiv  Detail & Related papers  (2021-01-29T20:54:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.