Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data
We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and port-Hamiltonian systems might share the same initial total energy of a closed system, it is challenging for a single Hamiltonian network model to capture the distinctive and varying motion dynamics and physics of a phase space, from sampled observational phase space trajectories. To address this complicated Hamiltonian manifold learning challenge, we extend sparse symplectic, random Fourier Gaussian processes learning with predictive successive numerical estimations of the Hamiltonian landscape, using a generalized form of state and conjugate momentum Hamiltonian dynamics, appropriate to different classes of conservative, dissipative and port-Hamiltonian physical systems. In addition to the kernelized evidence lower bound (ELBO) loss for data fidelity, we incorporate stability and conservation constraints as additional hyper-parameter balanced loss terms to regularize the model's multi-gradients, enforcing physics correctness for improved prediction accuracy with bounded uncertainty.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceGaussian ProcessesSimilar Papers 제목 키워드 기반
Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps …
Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data
Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. I…
Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes
Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have t…
Gaussian ProcessesDetecting Deepfakes via Hamiltonian Dynamics
Driven by the rapid development of generative AI models, deepfake detectors are compelled to undergo periodic recalibration to capture newly developed synthetic artifacts. To break this cycle, we propose a new perspectiv…
DeepFake DetectionAnomaly DetectionPort-Hamiltonian Koopman Operator Synthesis for Mechanical Systems
Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mec…