Related papers: NeuPDE: Neural Network Based Ordinary and Partial …
Many scientific phenomena are modeled by Partial Differential Equations (PDEs). The development of data gathering tools along with the advances in machine learning (ML) techniques have raised opportunities for data-driven identification of…
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…
Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of…
Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…
Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
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…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…