Related papers: Weak Form Generalized Hamiltonian Learning
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…
Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…
Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
Designing faster optimization algorithms is of ever-growing interest. In recent years, learning to learn methods that learn how to optimize demonstrated very encouraging results. Current approaches usually do not effectively include the…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation (GLE) with a homogeneous kernel. The constructed model naturally…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
In this work, we explore the use of compact latent representations with learned time dynamics ('World Models') to simulate physical systems. Drawing on concepts from control theory, we propose a theoretical framework that explains why…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…