Neural Context Flows for Meta-Learning of Dynamical Systems

2024-05-03

AI Summary

To address the failure of neural ordinary differential equations (NODEs) in out-of-distribution (OOD) generalization caused by implicit parameter shifts in physical systems, this paper proposes a meta-learning framework integrated with Bayesian uncertainty estimation. The core method introduces a novel context self-modulation mechanism based on Taylor expansion, enabling context vectors to dynamically adapt ODE dynamics across domains while performing self-calibration—ensuring both theoretical interpretability and robustness. The framework unifies context representation, NODE dynamics, and uncertainty quantification within a single probabilistic meta-learning architecture. Evaluated on six linear and nonlinear benchmark tasks, the approach achieves state-of-the-art OOD generalization performance on five. The implementation is open-sourced, facilitating transferable dynamical modeling in physical sciences.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications. Our code is openly available at https://github.com/ddrous/ncflow.

Problem

• Adapting NODEs to new dynamic behaviors with unobserved parameters.
• Improving adaptability and generalization in dynamical systems.
• Enhancing Out-of-Distribution performance in scientific applications.

Innovation

• Neural Context Flow for meta-learning adaptation
• Taylor expansion enables contextual self-modulation
• State-of-the-art Out-of-Distribution performance achieved