Related papers: ODE Test Problems: a MATLAB suite of initial value…
Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
Object-Oriented Programming (OOP) has become a crucial paradigm for managing the growing complexity of modern software systems, particularly in fields like machine learning, deep learning, large language models (LLM), and data analytics.…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
Investigation of detailed and complex optimisation problem formulations that reflect realistic scenarios is a burgeoning field of research. A growing body of work exists for the Travelling Thief Problem, including multi-objective…
In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) $y^{\prime}=p(y)$ over \emph{unbounded time domains}, where $p$ is a vector of polynomials. Contrarily to the bounded (compact) time…
Systematic testing of object-oriented software turned out to be much more complex than testing conventional software. Especially the highly incremental and iterative development cycle demands both many more changes and partially implemented…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
Deep learning (DL)-based systems can exhibit unexpected behavior when exposed to out-of-distribution (OOD) scenarios, posing serious risks in safety-critical domains such as malware detection and autonomous driving. This underscores the…
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…
We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE also…
Deep Learning (DL) compilers have been widely utilized to optimize DL models for efficient deployment across various hardware. Due to their vital role in the DL ecosystem, ensuring their reliability and security is critical. However,…
Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering…
Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Object-Oriented programming is frequently challenging for undergraduate Computer Science students, particularly in understanding abstract concepts such as encapsulation, inheritance, and polymorphism. Although the literature outlines…
A Marked Temporal Point Process (MTPP) is a stochastic process whose realization is a set of event-time data. MTPP is often used to understand complex dynamics of asynchronous temporal events such as money transaction, social media,…
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical…