Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations

2023/03/21 by Wenqian Chen, Panos Stinis, Chen, Wenqian +1 · 2 citations
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Heat Transfer and Optimization #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2303.11577

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to generate. To reduce or even eliminate the dependency on high-fidelity data, we propose a novel multi-fidelity architecture which is based on a feature space shared by the low- and high-fidelity solutions. In the feature space, the projections of the low-fidelity and high-fidelity solutions are adjacent by constraining their relative distance. The feature space is represented with an encoder and its mapping to the original solution space is effected through a decoder. The proposed multi-fidelity approach is validated on forward and inverse problems for steady and unsteady problems described by partial differential equations.

Cited by

• Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation
• Bridging quantum and classical computing for partial differential equations through multifidelity machine learning

Related

• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Enhancing Physics-Informed Neural Networks Through Feature Engineering
• MFPC-Net: Multi-fidelity Physics-Constrained Neural Process
• MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks
• Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations