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A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

In this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Gr\"unwald-Letnikov derivative. The infinite-history fractional-order system is approximated by a finite-dimensional…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

In this study, we present a purely data-driven method that uses the Loewner framework (LF) along with nonlinear optimization techniques to infer quadratic with affine control dynamical systems that admit Volterra series (VS) representations…

Model Order Reduction is a key technology for industrial applications in the context of digital twins. Key requirements are non-intrusiveness, physics-awareness, as well as robustness and usability. Operator inference based on least-squares…

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed…

Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…

Optimal power flow problems (OPFs) are mathematical programs used to determine how to distribute power over networks subject to network operation constraints and the physics of power flows. In this work, we take the view of treating an OPF…

Latent state space models are a fundamental and widely used tool for modeling dynamical systems. However, they are difficult to learn from data and learned models often lack performance guarantees on inference tasks such as filtering and…

Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. This is computationally demanding, particularly, if solutions have to be computed across strongly…

Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…