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An Extensible Benchmark Suite for Learning to Simulate Physical Systems
Karl Otness · Arvi Gjoka · Joan Bruna · Daniele Panozzo · Benjamin Peherstorfer · Teseo Schneider · Denis Zorin

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 to evaluate 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.

Author Information

Karl Otness (New York University)
Arvi Gjoka (New York University)
Joan Bruna (NYU)
Daniele Panozzo (NYU)
Benjamin Peherstorfer (New York University)
Teseo Schneider
Denis Zorin (New York University)

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