Related papers: Learning Neural Differential Algebraic Equations v…
Differential-algebraic equations (DAEs) arise naturally in constrained dynamical systems, but their algebraic constraints and hidden compatibility conditions make them more subtle than standard ordinary differential equations. This paper…
The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…
This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Neural ordinary differential equations (neural ODEs) can effectively learn dynamical systems from time series data, but their behavior on graph-structured data remains poorly understood, especially when applied to graphs with different size…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
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…
Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as…
Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challenging in machine learning. Integral equations (IEs), which…
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…
The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…
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,…
Dense associative memories (DAM), are widespread models in artificial intelligence used for pattern recognition tasks; computationally, they have been proven to be robust against adversarial input and theoretically, leveraging their analogy…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence.…