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Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are…
Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically…
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…
Physics-based computer models based on numerical solution of the governing equations generally cannot make rapid predictions, which in turn, limits their applications in the clinic. To address this issue, we developed a physics-informed…
In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy…
Reducing the computational time required by high-fidelity, full order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. While FOMs,…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…
Complex optimal design and control processes often require repeated evaluations of expensive objective functions and consist of large design spaces. Data-driven surrogates such as neural networks and Gaussian processes provide an attractive…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs). Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…
Underwater vehicles are employed in the exploration of dynamic environments where tuning of a specific controller for each task would be time-consuming and unreliable as the controller depends on calculated mathematical coefficients in…
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…