Related papers: Symbolic-numeric methods for improving structural …
As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems…
We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks. While deep learning has proven effective at modeling complex relationships from data, compositional couplings…
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…
We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…
We introduce a neuro-symbolic transformer-based model that converts flat, segmented facade structures into procedural definitions using a custom-designed split grammar. To facilitate this, we first develop a semi-complex split grammar…
Deriving analytical solutions of ordinary differential equations is usually restricted to a small subset of problems and numerical techniques are considered. Inevitably, a numerical simulation of a differential equation will then always be…
In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential…
In this thesis, we introduce the idea of combining symbolic execution with dynamic analysis for reverse engineering. Differently from DSE, we devise an approach where the reverse engineer can use a debugger to drive and inspect a concrete…
Structural analyses are an integral part of computational research on nucleation and supercooled water, whose accuracy and efficiency can impact the validity and feasibility of such studies. The underlying molecular mechanisms of these…
What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The…
Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…
In this paper, we study jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…
We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…
Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential…
Dynamic symbolic execution (DSE) is an effective method for automated program testing and bug detection. It is increasing the code coverage by the complex branches exploration during hybrid fuzzing. DSE tools invert the branches along some…