Related papers: Learning Dissipative Chaotic Dynamics with Bounded…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…

Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…

We present a novel method for guaranteeing linear momentum in learned physics simulations. Unlike existing methods, we enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional…

Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g.,…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative…

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

Neural networks have proven to be remarkably successful for a wide range of complicated tasks, from image recognition and object detection to speech recognition and machine translation. One of their successes is the skill in prediction of…

We study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…

We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…