Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures

• URL: http://arxiv.org/abs/2505.19521v2
• Date: Fri, 30 May 2025 01:41:54 GMT
• Title: Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures
• Abstract summary: This paper presents a geometric framework unifying measurements, constraints, and dynamics learning through a fiber bundle structure over the state space.<n>By integrating Neural ODEs, our framework learns continuous-time dynamics while preserving geometric constraints, with theoretical guarantees of learning convergence and constraint satisfaction dependent on sensing quality.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning unknown dynamics under environmental (or external) constraints is fundamental to many fields (e.g., modern robotics), particularly challenging when constraint information is only locally available and uncertain. Existing approaches requiring global constraints or using probabilistic filtering fail to fully exploit the geometric structure inherent in local measurements (by using, e.g., sensors) and constraints. This paper presents a geometric framework unifying measurements, constraints, and dynamics learning through a fiber bundle structure over the state space. This naturally induced geometric structure enables measurement-aware Control Barrier Functions that adapt to local sensing (or measurement) conditions. By integrating Neural ODEs, our framework learns continuous-time dynamics while preserving geometric constraints, with theoretical guarantees of learning convergence and constraint satisfaction dependent on sensing quality. The geometric framework not only enables efficient dynamics learning but also suggests promising directions for integration with reinforcement learning approaches. Extensive simulations demonstrate significant improvements in both learning efficiency and constraint satisfaction over traditional methods, especially under limited and uncertain sensing conditions.

Related papers

• The internal law of a material can be discovered from its boundary [4.3344158108954485]
  We introduce Neural-DFEM, a method that enables unsupervised discovery of hyperelastic material laws.<n>The method embeds a differentiable finite element solver within the learning loop, directly linking candidate energy functionals to available measurements.<n>Our results demonstrate that reliable identification of material laws is achievable even under partial observability.
  arXiv  Detail & Related papers  (2026-03-27T15:27:04Z)
• Reduced-order Control and Geometric Structure of Learned Lagrangian Latent Dynamics [16.958692029614994]
  This paper introduces a latent control framework based on learned structure-preserving reduced-order dynamics for high-dimensional Lagrangian systems.<n>By quantifying the sources of modeling error, we derive interpretable conditions for stability and convergence.<n>We extend the proposed controller and analysis to underactuated systems by introducing learned actuation patterns.
  arXiv  Detail & Related papers  (2026-02-09T18:00:04Z)
• Towards Worst-Case Guarantees with Scale-Aware Interpretability [58.519943565092724]
  Neural networks organize information according to the hierarchical, multi-scale structure of natural data.<n>We propose a unifying research agenda -- emphscale-aware interpretability -- to develop formal machinery and interpretability tools.
  arXiv  Detail & Related papers  (2026-02-05T01:22:31Z)
• Latent Space Reinforcement Learning for Multi-Robot Exploration [0.0]
  We develop a novel system for autonomous mapping of unknown environments.<n>We compress high-fidelity occupancy maps into latent state vectors while preserving essential spatial information.<n>We introduce a weighted consensus mechanism that modulates reliance on shared data.
  arXiv  Detail & Related papers  (2026-01-03T10:06:40Z)
• Adaptive Neighborhood-Constrained Q Learning for Offline Reinforcement Learning [52.03884701766989]
  offline reinforcement learning (RL) algorithms typically impose constraints on action selection.<n>We propose a new neighborhood constraint that restricts action selection in the Bellman target to the union of neighborhoods of dataset actions.<n>We develop a simple yet effective algorithm, Adaptive Neighborhood-constrained Q learning (ANQ), to perform Q learning with target actions satisfying this constraint.
  arXiv  Detail & Related papers  (2025-11-04T13:42:05Z)
• Physics-informed neural network solves minimal surfaces in curved spacetime [0.0]
  We develop a framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes.<n>Our approach enables robust and accurate solutions to both ordinary and partial differential equations with complex boundary conditions.
  arXiv  Detail & Related papers  (2025-09-13T15:41:13Z)
• Dynamic Manipulation of Deformable Objects in 3D: Simulation, Benchmark and Learning Strategy [88.8665000676562]
  Prior methods often simplify the problem to low-speed or 2D settings, limiting their applicability to real-world 3D tasks.<n>To mitigate data scarcity, we introduce a novel simulation framework and benchmark grounded in reduced-order dynamics.<n>We propose Dynamics Informed Diffusion Policy (DIDP), a framework that integrates imitation pretraining with physics-informed test-time adaptation.
  arXiv  Detail & Related papers  (2025-05-23T03:28:25Z)
• TamedPUMA: safe and stable imitation learning with geometric fabrics [14.885339698387991]
  Imitation learning (IL) provides an intuitive and effective way of teaching stable task-space motions to robots with goal convergence.<n>With this work, we solve this challenge via TamedPUMA, an IL algorithm augmented with a recent development in motion generation called geometric fabrics.<n>The result is a stable imitation learning strategy within which we can seamlessly blend geometrical constraints like collision avoidance and joint limits.
  arXiv  Detail & Related papers  (2025-03-21T13:13:17Z)
• Form-Finding and Physical Property Predictions of Tensegrity Structures Using Deep Neural Networks [39.19016806159609]
  We develop a deep neural network (DNN) approach to predict the geometric configurations and physical properties of tensegrity structures. For validation, we analyze three tensegrity structures, including a tensegrity D-bar, prism, and lander.
  arXiv  Detail & Related papers  (2024-06-15T16:39:53Z)
• Neural Fields with Hard Constraints of Arbitrary Differential Order [61.49418682745144]
  We develop a series of approaches for enforcing hard constraints on neural fields. The constraints can be specified as a linear operator applied to the neural field and its derivatives. Our approaches are demonstrated in a wide range of real-world applications.
  arXiv  Detail & Related papers  (2023-06-15T08:33:52Z)
• Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics [96.9177297872723]
  We present a novel method for guaranteeing linear momentum in learned physics simulations. We enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially.
  arXiv  Detail & Related papers  (2022-10-12T09:12:59Z)
• Failure-averse Active Learning for Physics-constrained Systems [7.701064815584088]
  We develop a novel active learning method that avoids failures considering implicit physics constraints that govern the system. The proposed approach is driven by two tasks: the safe variance reduction explores the safe region to reduce the variance of the target model, and the safe region expansion aims to extend the explorable region exploiting the probabilistic model of constraints. The method is applied to the composite fuselage assembly process with consideration of material failure using the Tsai-wu criterion, and it is able to achieve zero-failure without the knowledge of explicit failure regions.
  arXiv  Detail & Related papers  (2021-10-27T14:01:03Z)
• Adaptive Surface Normal Constraint for Depth Estimation [102.7466374038784]
  We introduce a simple yet effective method, named Adaptive Surface Normal (ASN) constraint, to correlate the depth estimation with geometric consistency. Our method can faithfully reconstruct the 3D geometry and is robust to local shape variations, such as boundaries, sharp corners and noises.
  arXiv  Detail & Related papers  (2021-03-29T10:36:25Z)
• An Integer Linear Programming Framework for Mining Constraints from Data [81.60135973848125]
  We present a general framework for mining constraints from data. In particular, we consider the inference in structured output prediction as an integer linear programming (ILP) problem. We show that our approach can learn to solve 9x9 Sudoku puzzles and minimal spanning tree problems from examples without providing the underlying rules.
  arXiv  Detail & Related papers  (2020-06-18T20:09:53Z)
• Plan-Space State Embeddings for Improved Reinforcement Learning [12.340412143459869]
  We present a new method for learning state embeddings from plans or other forms of demonstrations. We show how these embeddings can then be used as an augmentation to the robot state in reinforcement learning problems.
  arXiv  Detail & Related papers  (2020-04-30T03:38:14Z)
• Local Propagation in Constraint-based Neural Network [77.37829055999238]
  We study a constraint-based representation of neural network architectures. We investigate a simple optimization procedure that is well suited to fulfil the so-called architectural constraints.
  arXiv  Detail & Related papers  (2020-02-18T16:47:38Z)

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.