Related papers: Hybrid Symbolic-Numeric Framework for Power System…
Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical…
Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…
With growing intermittency and uncertainty in distribution networks around the world, ensuring operational integrity is becoming challenging. Recent use cases of dynamic operating envelopes (DOEs) indicate that they can be utilized for…
Thermodynamic equations of state (EOS) are essential for many industries as well as in academia. Even leaving aside the expensive and extensive measurement campaigns required for the data acquisition, the development of EOS is an intensely…
An algebraic modeling system (AMS) is a type of mathematical software for optimization problems, which allows users to define symbolic mathematical models in a specific language, instantiate them with given source of data, and solve them…
Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven methods demand costly labeled datasets while model-driven…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based…
The rapid proliferation of distributed energy resources (DERs) and the electrification of residential loads offer significant potential for grid flexibility but pose stability challenges under static pricing regimes. Specifically, high…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
High fidelity design evaluation processes such as Computational Fluid Dynamics and Finite Element Analysis are often replaced with data driven surrogates to reduce computational cost in engineering design optimization. However, building…
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra…
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…
In the design phase of an electrical machine, finite element (FE) simulation are commonly used to numerically optimize the performance. The output of the magneto-static FE simulation characterizes the electromagnetic behavior of the…
This work systematically investigates the performance of FORCE--$\alpha$ numerical fluxes within an arbitrary high order semidiscrete finite volume (FV) framework for hyperbolic partial differential equations (PDEs). Such numerical fluxes…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…
In this paper, we investigate Kolmogorov-Arnold network-based autoencoders (KAN-AEs) with symbolic regression (SR) for energy-efficient channel coding. By using SR, we convert KAN-AEs into symbolic expressions, which enables low-complexity…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
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…