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Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress…

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

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…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…

Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…

This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

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…

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed…

The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…

In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…

Dynamic astrophysical phenomena are predominantly described by differential equations, yet our understanding of these systems is constrained by our incomplete grasp of non-linear physics and scarcity of comprehensive datasets. As such,…