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In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited…

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately,…

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…

Differentiable Programming for scientific machine learning (SciML) has recently seen considerable interest and success, as it directly embeds neural networks inside PDEs, often called as NeuralPDEs, derived from first principle physics.…

Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs…

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest…

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…

Proportional-Integral-Derivative (PID) control is used for automatically regulating a measurable quantity to a desired setpoint. It is widely used in different types of classical control electronics. Here, we show how extending the feedback…

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…

Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…

Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…

Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…

We present the concepts of physics-based learning models (PBLM) and their relevance and application to the field of ship hydrodynamics. The utility of physics-based learning is motivated by contrasting generic learning models for regression…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…