相关论文: Recovering the state and dynamics of autonomous sy…

A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the…

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…

This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…