Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models

• URL: http://arxiv.org/abs/2106.11609v1
• Date: Tue, 22 Jun 2021 08:40:51 GMT
• Title: Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models
• Authors: Lenart Treven, Philippe Wenk, Florian D\"orfler, Andreas Krause
• Abstract summary: We propose a novel approach towards estimating uncertain neural ODEs, avoiding the numerical integration bottleneck. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.
• Score: 38.17499046781131
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

Related papers

• Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets [0.0]
  We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. We perform Inverse Modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. We formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations.
  arXiv  Detail & Related papers  (2023-03-31T06:47:02Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEs [22.976119802895017]
  We propose a data-driven approach to the training of neural ordinary differential equations (NODEs) The proposed approach achieves the same accuracy as adaptive step-size schemes while employing only low-order Taylor expansions. A suite of numerical experiments demonstrate that TL-NODEs can be trained more than an order of magnitude faster than state-of-the-art approaches.
  arXiv  Detail & Related papers  (2022-01-14T23:56:19Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• STEER: Simple Temporal Regularization For Neural ODEs [80.80350769936383]
  We propose a new regularization technique: randomly sampling the end time of the ODE during training. The proposed regularization is simple to implement, has negligible overhead and is effective across a wide variety of tasks. We show through experiments on normalizing flows, time series models and image recognition that the proposed regularization can significantly decrease training time and even improve performance over baseline models.
  arXiv  Detail & Related papers  (2020-06-18T17:44:50Z)
• Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness [24.473250414880454]
  We study principled approaches to high-quality uncertainty estimation that require only a single deep neural network (DNN) By formalizing the uncertainty quantification as a minimax learning problem, we first identify input distance awareness, i.e., the model's ability to quantify the distance of a testing example from the training data in the input space. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs.
  arXiv  Detail & Related papers  (2020-06-17T19:18:22Z)
• A Deterministic Approximation to Neural SDEs [38.23826389188657]
  We show that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. We develop a computationally affordable deterministic scheme which accurately approximates the transition kernel. Our method also improves prediction accuracy thanks to the numerical stability of deterministic training.
  arXiv  Detail & Related papers  (2020-06-16T08:00:26Z)
• Path Sample-Analytic Gradient Estimators for Stochastic Binary Networks [78.76880041670904]
  In neural networks with binary activations and or binary weights the training by gradient descent is complicated. We propose a new method for this estimation problem combining sampling and analytic approximation steps. We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional models.
  arXiv  Detail & Related papers  (2020-06-04T21:51:21Z)
• Interpolation Technique to Speed Up Gradients Propagation in Neural ODEs [71.26657499537366]
  We propose a simple literature-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method to train neural ODEs on classification, density estimation, and inference approximation tasks.
  arXiv  Detail & Related papers  (2020-03-11T13:15:57Z)
• Stochasticity in Neural ODEs: An Empirical Study [68.8204255655161]
  Regularization of neural networks (e.g. dropout) is a widespread technique in deep learning that allows for better generalization. We show that data augmentation during the training improves the performance of both deterministic and versions of the same model. However, the improvements obtained by the data augmentation completely eliminate the empirical regularization gains, making the performance of neural ODE and neural SDE negligible.
  arXiv  Detail & Related papers  (2020-02-22T22:12:56Z)

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.