相关论文: Model-agnostic machine learning of conservation la…

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

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 tackled the problem…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

Machine-learning models are ubiquitous. In some domains, for instance, in medicine, the models' predictions must be interpretable. Decision trees, classification rules, and subgroup discovery are three broad categories of supervised…

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…

The use of multiple Decision Models (DMs) enables to enhance the accuracy in decisions and at the same time allows users to evaluate the confidence in decision making. In this paper we explore the ability of multiple DMs to learn from a…

We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…

This paper addresses the problem of inferring a hybrid automaton from a set of input-output traces of a hybrid system exhibiting discrete mode switching between continuously evolving dynamics. Existing approaches mainly adopt a…

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…

Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…