Related papers: Using scientific machine learning for experimental…

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…

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…

Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…

This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits…

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

The n body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learning models that are used for predicting and forecasting…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…

Universal Differential Equations (UDEs), which blend neural networks with physical differential equations, have emerged as a powerful framework for scientific machine learning (SciML), enabling data-efficient, interpretable, and physically…

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…

We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…

The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…