Reduced Operator Inference for Nonlinear Partial Differential Equations
نویسندگان
چکیده
We present a new scientific machine learning method that learns from data computationally inexpensive surrogate model for predicting the evolution of system governed by time-dependent nonlinear partial differential equation (PDE), an enabling technology many computational algorithms used in engineering settings. Our formulation generalizes to function space PDE setting Operator Inference previously developed [B. Peherstorfer and K. Willcox, Comput. Methods Appl. Mech. Engrg., 306 (2016), pp. 196--215] systems ordinary equations. The brings together two main elements. First, ideas projection-based reduction are explicitly parametrize learned low-dimensional polynomial operators which reflect known form governing PDE. Second, supervised tools infer reduced this physics-informed parametrization. For whose PDEs contain more general (nonpolynomial) nonlinearities, performance can be improved through use lifting variable transformations, expose structure proposed is demonstrated on examples: heat problem demonstrates benefits terms consistency with underlying continuous truth, three-dimensional combustion simulation over 18 million degrees freedom, models achieve accurate predictions dimension five orders magnitude runtime up nine magnitude.
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2022
ISSN: ['1095-7197', '1064-8275']
DOI: https://doi.org/10.1137/21m1393972