Physics-informed neural networks via stochastic Hamiltonian dynamics learning

• URL: http://arxiv.org/abs/2111.08108v3
• Date: Fri, 26 Apr 2024 05:10:50 GMT
• Title: Physics-informed neural networks via stochastic Hamiltonian dynamics learning
• Abstract summary: We propose novel learning frameworks to tackle optimal control problems. Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to reduced Hamiltonian dynamics. We apply our learning frameworks called NeuralPMP to various control tasks and obtain competitive results.
• Score: 3.2857981869020327
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to reduced Hamiltonian dynamics and corresponding adjoint variables. Then, the reduced Hamiltonian networks can be learned by going backwards in time and then minimizing loss function deduced from the Pontryagin maximum principle's conditions. The learning process is further improved by progressively learning a posterior distribution of the reduced Hamiltonians. This is achieved through utilizing a variational autoencoder which leads to more effective path exploration process. We apply our learning frameworks called NeuralPMP to various control tasks and obtain competitive results.

Related papers

• End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagation [0.8244545230770907]
  We propose an end-to-end implicit deep learning approach that directly parameterizes the value function to learn optimal control laws.<n>We show that our approach effectively learns high-dimensional feedback controllers across multiple scenarios involving implicit Hamiltonians.
  arXiv  Detail & Related papers  (2025-10-01T00:03:08Z)
• Probabilistic Pontryagin's Maximum Principle for Continuous-Time Model-Based Reinforcement Learning [3.6300632181659234]
  We show that minimization of the mean Hamiltonian is a necessary optimality condition when optimizing the mean cost. Our approach offers a principled and practical framework for controlling uncertain systems with learned dynamics.
  arXiv  Detail & Related papers  (2025-04-03T12:51:20Z)
• A Unified Framework for Neural Computation and Learning Over Time [56.44910327178975]
  Hamiltonian Learning is a novel unified framework for learning with neural networks "over time" It is based on differential equations that: (i) can be integrated without the need of external software solvers; (ii) generalize the well-established notion of gradient-based learning in feed-forward and recurrent networks; (iii) open to novel perspectives.
  arXiv  Detail & Related papers  (2024-09-18T14:57:13Z)
• Neural Time-Reversed Generalized Riccati Equation [60.92253836775246]
  Hamiltonian equations offer an interpretation of optimality through auxiliary variables known as costates. This paper introduces a novel neural-based approach to optimal control, with the aim of working forward-in-time.
  arXiv  Detail & Related papers  (2023-12-14T19:29:37Z)
• The least-control principle for learning at equilibrium [65.2998274413952]
  We present a new principle for learning equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.
  arXiv  Detail & Related papers  (2022-07-04T11:27:08Z)
• Practical Black Box Hamiltonian Learning [0.9281671380673306]
  We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. We build upon recent approaches to Hamiltonian learning via derivative estimation.
  arXiv  Detail & Related papers  (2022-06-30T17:56:14Z)
• Learning Neural Hamiltonian Dynamics: A Methodological Overview [109.40968389896639]
  Hamiltonian dynamics endows neural networks with accurate long-term prediction, interpretability, and data-efficient learning. We systematically survey recently proposed Hamiltonian neural network models, with a special emphasis on methodologies.
  arXiv  Detail & Related papers  (2022-02-28T22:54:39Z)
• A control method for solving high-dimensional Hamiltonian systems through deep neural networks [0.2752817022620644]
  We first introduce a corresponding optimal control problem such that the Hamiltonian system of control problem is exactly what we need to solve, then develop two different algorithms suitable for different cases of the control problem and approximate the control via deep neural networks. From the numerical results, comparing with the Deep FBSDE method which was developed previously from the view of solving FBSDEs, the novel algorithms converge faster, which means that they require fewer training steps, and demonstrate more stable convergences for different Hamiltonian systems.
  arXiv  Detail & Related papers  (2021-11-04T05:22:08Z)
• Can we learn gradients by Hamiltonian Neural Networks? [68.8204255655161]
  We propose a meta-learner based on ODE neural networks that learns gradients. We demonstrate that our method outperforms a meta-learner based on LSTM for an artificial task and the MNIST dataset with ReLU activations in the optimizee.
  arXiv  Detail & Related papers  (2021-10-31T18:35:10Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Symplectic Learning for Hamiltonian Neural Networks [0.0]
  Hamiltonian Neural Networks (HNNs) took a first step towards a unified "gray box" approach. We exploit the symplectic structure of Hamiltonian systems with a different loss function. We mathematically guarantee the existence of an exact Hamiltonian function which the HNN can learn.
  arXiv  Detail & Related papers  (2021-06-22T13:33:12Z)
• Hamiltonian neural networks for solving equations of motion [3.1498833540989413]
  We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. A symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network in order to achieve the same order of the numerical error.
  arXiv  Detail & Related papers  (2020-01-29T21:48:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.