Related papers: Energy-Preserving Reduced Operator Inference for E…

Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained…

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where…

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases…

Predictive maintenance is an effective tool for reducing maintenance costs. Its effectiveness relies heavily on the ability to predict the future state of health of the system, and for this survival models have shown to be very useful. Due…

Energy is now a first-class design constraint along with performance in all computing settings. Energy predictive modelling based on performance monitoring counts (PMCs) is the leading method used for prediction of energy consumption during…

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics…

In many science and engineering settings, system dynamics are characterized by governing PDEs, and a major challenge is to solve inverse problems (IPs) where unknown PDE parameters are inferred based on observational data gathered under…

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups with various state parameters. In traditional numerical methods, each problem is solved independently, resulting in many…

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

Partially observable Markov decision processes (POMDPs) are a powerful abstraction for tasks that require decision making under uncertainty, and capture a wide range of real world tasks. Today, effective planning approaches exist that…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have…

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…

Urban wastewater sector is being pushed to optimize processes in order to reduce energy consumption without compromising its quality standards. Energy costs can represent a significant share of the global operational costs (between 50% and…

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

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…

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…