Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations
This addresses the challenge of building interpretable and generalizable surrogate models for stochastic simulators, particularly in domains like physics and engineering, though it appears incremental as it builds on existing methods like CMMD loss.
The paper tackles the problem of modeling physical systems governed by stochastic differential equations by proposing the Deep Physics Corrector, which combines approximate physics with deep neural networks to model missing physics, achieving highly accurate results on four benchmark examples.
We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms of SDE with deep neural network (DNN). The primary idea here is to exploit DNN to model the missing physics. We hypothesize that combining incomplete physics with data will make the model interpretable and allow better generalization. The primary bottleneck associated with training surrogate models for stochastic simulators is often associated with selecting the suitable loss function. Among the different loss functions available in the literature, we use the conditional maximum mean discrepancy (CMMD) loss function in DPC because of its proven performance. Overall, physics-data fusion and CMMD allow DPC to learn from sparse data. We illustrate the performance of the proposed DPC on four benchmark examples from the literature. The results obtained are highly accurate, indicating its possible application as a surrogate model for stochastic simulators.