Encoding physics to learn reaction-diffusion processes
- URL: http://arxiv.org/abs/2106.04781v2
- Date: Mon, 22 May 2023 06:14:15 GMT
- Title: Encoding physics to learn reaction-diffusion processes
- Authors: Chengping Rao, Pu Ren, Qi Wang, Oral Buyukozturk, Hao Sun, Yang Liu
- Abstract summary: We show how a deep learning framework that encodes given physics structure can be applied to a variety of problems regarding the PDE system regimes.
The resultant learning paradigm that encodes physics shows high accuracy, robustness, interpretability and generalizability demonstrated via extensive numerical experiments.
- Score: 18.187800601192787
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Modeling complex spatiotemporal dynamical systems, such as the
reaction-diffusion processes, have largely relied on partial differential
equations (PDEs). However, due to insufficient prior knowledge on some
under-explored dynamical systems, such as those in chemistry, biology, geology,
physics and ecology, and the lack of explicit PDE formulation used for
describing the nonlinear process of the system variables, to predict the
evolution of such a system remains a challenging task. Unifying measurement
data and our limited prior physics knowledge via machine learning provides us
with a new path to solving this problem. Existing physics-informed learning
paradigms impose physics laws through soft penalty constraints, whose solution
quality largely depends on a trial-and-error proper setting of hyperparameters.
Since the core of such methods is still rooted in black-box neural networks,
the resulting model generally lacks interpretability and suffers from critical
issues of extrapolation and generalization. To this end, we propose a deep
learning framework that forcibly encodes given physics structure to facilitate
the learning of the spatiotemporal dynamics in sparse data regimes. We show how
the proposed approach can be applied to a variety of problems regarding the PDE
system, including forward and inverse analysis, data-driven modeling, and
discovery of PDEs. The resultant learning paradigm that encodes physics shows
high accuracy, robustness, interpretability and generalizability demonstrated
via extensive numerical experiments.
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