Related papers: Index Reduction for Differential-Algebraic Equatio…

For large-scale discrete-time algebraic Riccati equations (DAREs) with high-rank nonlinear and constant terms, the stabilizing solutions are no longer numerically low-rank, resulting in the obstacle in the computation and storage. However,…

Imbalanced distribution learning is a common and significant challenge in predictive modeling, often reducing the performance of standard algorithms. Although various approaches address this issue, most are tailored to classification…

This paper introduces a methodology based on Denoising AutoEncoder (DAE) for missing data imputation. The proposed methodology, called mDAE hereafter, results from a modification of the loss function and a straightforward procedure for…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Autograd-based software packages have recently renewed interest in image registration using homography and other geometric models by gradient descent and optimization, e.g., AirLab and DRMIME. In this work, we emphasize on using complex…

The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…

In machine learning forecasting, standard error metrics such as mean absolute error (MAE) and mean squared error (MSE) quantify discrepancies between predictions and target values. However, these metrics do not directly evaluate the…

Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…

This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…

In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

It is a general notion that, in transient stability simulations, reducing the number of algebraic variables for the differential-algebraic equations (DAE) can improve the simulation performance. Many simulation programs split algebraic…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…

Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…

Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…

We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and…