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Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
The time-domain analysis of pulse width modulated (PWM) single-phase inverters is presented for different load circuits. It is demonstrated that this analysis can be reduced to the solution of linear simultaneous algebraic equations with…
Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…
This paper proposes a distributed diagnosis scheme to detect and estimate actuator and power line faults in DC microgrids (e.g., electric-vehicle charging microgrids) subject to unknown power loads and stochastic noise. To address actuator…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential…
Many Partial Differential Equations (PDEs) do not have analytical solution, and can only be solved by numerical methods. In this context, Physics-Informed Neural Networks (PINN) have become important in the last decades, since it uses a…
Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of…
The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field…
Large scale circuit simulation, such as power delivery network analysis, has become increasingly challenge in the VLSI design verification flow. Power delivery network can be simulated by both SPICE-type circuit-based model and…
In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method…
This paper presents the design and analysis of a high efficiency, PWM (Pulse-Width-Modulation) Buck converters for mobile phone applications. The steady-state and average-value models for the proposed converter are developed and simulated.…
We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…
Deep neural networks have garnered widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this study, we probe into solving a class of elliptic partial differential…
The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an…
The simulation of radio frequency (RF) circuits is one of the severest problems in Design Automation: the information signal or envelope is modulated by a carrier signal with a center frequency typically in the GHz range. Due to Nyquist's…
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we…
A modulated model predictive controller is designed for an inductor-less modular multilevel converter targeting an MVDC solid-state transformer application. The underlying optimization problem is formulated such that a unique closed-form…
Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.
The method of separation of variables can be used to solve many separable linear partial differential equations (LPDEs). Moreover, variable separation solutions usually are some trigonometric series. In the paper, base on some ideas of this…