Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

Abstract

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.

References in corpus (11)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• How to train your neural ODE: the world of Jacobian and kinetic regularization
• Deep learning of thermodynamics-aware reduced-order models from data
• Structure-preserving neural networks
• Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
• Lagrangian Neural Networks
• Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE
• Turbulence forecasting via Neural ODE
• Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems

Cited by in corpus (7)

• Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations
• Deep Learning the Functional Renormalization Group
• Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models
• Metalearning generalizable dynamics from trajectories
• NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regions
• Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcations
• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives