An Extensible Benchmark Suite for Learning to Simulate Physical Systems

2021/08/09 by Karl Otness, Arvi Gjoka, Otness, Karl +11 · 4 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Heat Transfer and Optimization #Machine Learning (cs.LG) #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2108.07799

openalex publication_date 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations methods, motivated by the opportunity to reduce computational costs and/or learn new physical models leveraging access to large collections of data. However, the diversity of problem settings and applications has led to a plethora of approaches, each one evaluated on a different setup and with different evaluation metrics. We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time integrators and representative data-driven methods (kernel-based, MLP, CNN, nearest neighbors). Our framework allows evaluating objectively and systematically the stability, accuracy, and computational efficiency of data-driven methods. Additionally, it is configurable to permit adjustments for accommodating other learning tasks and for establishing a foundation for future developments in machine learning for scientific computing.

Citations

• Symplectic Model Reduction of Hamiltonian Systems
• Matplotlib: A 2D Graphics Environment
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Hamiltonian Graph Networks with ODE Integrators
• Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil Flows
• Discovering Symbolic Models from Deep Learning with Inductive Biases

Cited by

• MDBench: Benchmarking Data-Driven Methods for Model Discovery
• Diffusion Models for Time Series Forecasting: A Survey
• Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics
• Geometric Contact Flows: Contactomorphisms for Dynamics and Control

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• Scientific Machine Learning Benchmarks
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• On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods
• Factorized Machine Learning for Performance Modeling of Massively Parallel Heterogeneous Physical Simulations