 Award ID(s):
 2214939
 NSFPAR ID:
 10522938
 Editor(s):
 Matni, Nikolai; Morari, Manfred; Pappas, George J
 Publisher / Repository:
 Learning for Dynamics and Control Conference
 Date Published:
 Volume:
 211
 Page Range / eLocation ID:
 679691
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Firoozi, R. ; Mehr, N. ; Yel, E. ; Antonova, R. ; Bohg, J. ; Schwager, M. ; Kochenderfer, M. (Ed.)Effective inclusion of physicsbased knowledge into deep neural network models of dynamical sys tems can greatly improve data efficiency and generalization. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or from the system’s design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a priori system knowledge as inductive bias. More specifically, the proposed framework uses physicsbased side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system’s vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physicsinformed constraints are enforced via the augmented Lagrangian method during the model’s training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems – including a benchmark suite of robotics environments featur ing large state spaces, nonlinear dynamics, external forces, contact forces, and control inputs. By exploiting a priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.more » « less

Physicsinspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world systems, such as those that don’t conserve energy or contain contacts, a common setting for robotics and reinforcement learning. In this paper, we examine the inductive biases that make physicsinspired models successful in practice. We show that, contrary to conventional wisdom, the improved generalization of HNNs is the result of modeling acceleration directly and avoiding artificial complexity from the coordinate system, rather than symplectic structure or energy conservation. We show that by relaxing the inductive biases of these models, we can match or exceed performance on energyconserving systems while dramatically improving performance on practical, nonconservative systems. We extend this approach to constructing transition models for common Mujoco environments, showing that our model can appropriately balance inductive biases with the flexibility required for modelbased control.more » « less

Recent advancements in physicsinformed machine learning have contributed to solving partial differential equations through means of a neural network. Following this, several physicsinformed neural network works have followed to solve inverse problems arising in structural health monitoring. Other works involving physicsinformed neural networks solve the wave equation with partial data and modeling wavefield data generator for efficient sound data generation. While a lot of work has been done to show that partial differential equations can be solved and identified using a neural network, little work has been done the same with more basic machine learning (ML) models. The advantage with basic ML models is that the parameters learned in a simpler model are both more interpretable and extensible. For applications such as ultrasonic nondestructive evaluation, this interpretability is essential for trustworthiness of the methods and characterization of the material system under test. In this work, we show an interpretable, physicsinformed representation learning framework that can analyze data across multiple dimensions (e.g., two dimensions of space and one dimension of time). The algorithm comes with convergence guarantees. In addition, our algorithm provides interpretability of the learned model as the parameters correspond to the individual solutions extracted from data. We demonstrate how this algorithm functions with wavefield videos.more » « less

Abstract The method of choice for integrating the timedependent Fokker–Planck equation (FPE) in highdimension is to generate samples from the solution via integration of the associated stochastic differential equation (SDE). Here, we study an alternative scheme based on integrating an ordinary differential equation that describes the flow of probability. Acting as a transport map, this equation deterministically pushes samples from the initial density onto samples from the solution at any later time. Unlike integration of the stochastic dynamics, the method has the advantage of giving direct access to quantities that are challenging to estimate from trajectories alone, such as the probability current, the density itself, and its entropy. The probability flow equation depends on the gradient of the logarithm of the solution (its ‘score’), and so is
apriori unknown. To resolve this dependence, we model the score with a deep neural network that is learned onthefly by propagating a set of samples according to the instantaneous probability current. We show theoretically that the proposed approach controls the Kullback–Leibler (KL) divergence from the learned solution to the target, while learning on external samples from the SDE does not control either direction of the KL divergence. Empirically, we consider several highdimensional FPEs from the physics of interacting particle systems. We find that the method accurately matches analytical solutions when they are available as well as moments computed via MonteCarlo when they are not. Moreover, the method offers compelling predictions for the global entropy production rate that outperform those obtained from learning on stochastic trajectories, and can effectively capture nonequilibrium steadystate probability currents over long time intervals. 
Training machine learning (ML) models for scientific problems is often challenging due to limited observation data. To overcome this challenge, prior works commonly pretrain ML models using simulated data before having them finetuned with small real data. Despite the promise shown in initial research across different domains, these methods cannot ensure improved performance after finetuning because (i) they are not designed for extracting generalizable physicsaware features during pretraining, (ii) the features learned from pretraining can be distorted by the finetuning process. In this paper, we propose a new learning method for extracting, preserving, and adapting physicsaware features. We build a knowledgeguided neural network (KGNN) model based on known dependencies amongst physical variables, which facilitate extracting physicsaware feature representation from simulated data. Then we finetune this model by alternately updating the encoder and decoder of the KGNN model to enhance the prediction while preserving the physicsaware features learned through pretraining. We further propose to adapt the model to new testing scenarios via a teacherstudent learning framework based on the model uncertainty. The results demonstrate that the proposed method outperforms many baselines by a good margin, even using sparse training data or under outofsample testing scenarios.more » « less