Homotopy-based training of NeuralODEs for accurate dynamics discovery

• URL: http://arxiv.org/abs/2210.01407v6
• Date: Tue, 23 Jan 2024 05:44:22 GMT
• Title: Homotopy-based training of NeuralODEs for accurate dynamics discovery
• Authors: Joon-Hyuk Ko, Hankyul Koh, Nojun Park, Wonho Jhe
• Abstract summary: We develop a new training method for NeuralODEs, based on synchronization and homotopy optimization. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape. Our method achieves competitive or better training loss while often requiring less than half the number of training epochs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. However, these models often display long training times and suboptimal results, especially for longer duration data. While a common strategy in the literature imposes strong constraints to the NeuralODE architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. In this paper, we develop a new training method for NeuralODEs, based on synchronization and homotopy optimization, that does not require changes to the model architecture. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. Through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. Furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method.

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• Towards Efficient Modelling of String Dynamics: A Comparison of State Space and Koopman based Deep Learning Methods [8.654571696634825]
  State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Our findings indicate that our proposed Koopman-based model performs as well as or better than other existing approaches in non-linear cases for long-sequence modelling. This research contributes insights into the physical modelling of dynamical systems by offering a comparative overview of these and previous methods and introducing innovative strategies for model improvement.
  arXiv  Detail & Related papers  (2024-08-29T15:55:27Z)
• Semi-Supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach [10.20098335268973]
  TS-NODE is the first semi-supervised approach to modeling dynamical systems with NODE. We show significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.
  arXiv  Detail & Related papers  (2023-10-19T19:17:12Z)
• Gradient-Based Trajectory Optimization With Learned Dynamics [80.41791191022139]
  We use machine learning techniques to learn a differentiable dynamics model of the system from data. We show that a neural network can model highly nonlinear behaviors accurately for large time horizons. In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car.
  arXiv  Detail & Related papers  (2022-04-09T22:07:34Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Sparse Flows: Pruning Continuous-depth Models [107.98191032466544]
  We show that pruning improves generalization for neural ODEs in generative modeling. We also show that pruning finds minimal and efficient neural ODE representations with up to 98% less parameters compared to the original network, without loss of accuracy.
  arXiv  Detail & Related papers  (2021-06-24T01:40:17Z)
• Accelerating Neural ODEs Using Model Order Reduction [0.0]
  We show that mathematical model order reduction methods can be used for compressing and accelerating Neural ODEs. We implement our novel compression method by developing Neural ODEs that integrate the necessary subspace-projection and operations as layers of the neural network.
  arXiv  Detail & Related papers  (2021-05-28T19:27:09Z)
• DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control [0.0]
  We present a novel approach that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. Results indicate that a simple DyNODE architecture when combined with an actor-critic reinforcement learning algorithm outperforms canonical neural networks.
  arXiv  Detail & Related papers  (2020-09-09T12:56:58Z)
• Model-based Reinforcement Learning for Semi-Markov Decision Processes with Neural ODEs [30.36381338938319]
  We present two solutions for modeling continuous-time dynamics using neural ordinary differential equations (ODEs) Our models accurately characterize continuous-time dynamics and enable us to develop high-performing policies using a small amount of data. We experimentally demonstrate the efficacy of our methods across various continuous-time domains.
  arXiv  Detail & Related papers  (2020-06-29T17:21:43Z)
• 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.