Enforcing Analytic Constraints in Neural Networks Emulating Physical Systems.

By Tom Beucler, Michael S. Pritchard, Stephan Rasp, J. Ott, Pierre Baldi, Pierre Gentine. Physical Review Letters, 2019

364 citations recorded by the source corpus.

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to convective processes for climate modeling, architectural constraints enforce conservation laws to within machine precision without degrading performance. Enforcing constraints also reduces errors in the subsets of the outputs most impacted by the constraints.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ed53d03140c59c18dedd27bb2740467a02988b71

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Citations in the corpus

Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “show that enforcing energy conservation laws improves prediction when emulating cloud processes [31, 32].”
Towards Physics-informed Deep Learning for Turbulent Flow Prediction (2019, background): “[34, 38] introduced statistical and physical constraints in the loss function to regularize the predictions for emulating physical simulations.”
What Role Does Hydrological Science Play in the Age of Machine Learning? (2020, methodology): “From an ML perspective, this is a regularization problem, and common methods include things like (e.g., Pelissier et al., 2020; Rackauckas et al., 2020), and (iii) architecturally constrained neural networks (e.g., Beucler et al., 2019; Daw et al., 2020).”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, methodology): “…existing work uses standard black box ML models for parameterization, but there is an increasing interest in integrating physics in the ML models [23], as it has the potential to make them more robust and generalizable to unseen scenarios as well as reduce the number of training samples needed…”