Related papers: Deriving Analytical Solutions Using Symbolic Matri…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
We describe our work on inferring the degrees of freedom between mated parts in mechanical assemblies using deep learning on CAD representations. We train our model using a large dataset of real-world mechanical assemblies consisting of CAD…
Explainable AI aims to render model behavior understandable by humans, which can be seen as an intermediate step in extracting causal relations from correlative patterns. Due to the high risk of possible fatal decisions in image-based…
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…
Structural equation models (SEMs) are widely used in sciences, ranging from economics to psychology, to uncover causal relationships underlying a complex system under consideration and estimate structural parameters of interest. We study…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
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…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Analyzing non-compilable C/C++ submodules without a resolved build environment remains a critical bottleneck for industrial software evolution. Traditional static analysis tools often fail in these scenarios due to their reliance on…
This paper presents NEUROSPF, a tool for the symbolic analysis of neural networks. Given a trained neural network model, the tool extracts the architecture and model parameters and translates them into a Java representation that is amenable…
A complete approach to reasoning under uncertainty requires support for incremental and interactive formulation and revision of, as well as reasoning with, models of the problem domain capable of representing our uncertainty. We present a…
The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear…
Understanding how prices evolve over time often requires peeling back the layers of market noise to identify clear, structural behavior. Many of the tools commonly used for this purpose technical indicators, chart heuristics, or even…
Static program analysis plays an essential role in program optimization, bug detection, and debugging. However, reliance on compilation and limited customization hinder its adoption in the real world. This paper presents a compositional…
Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…
Two-fold redundant sparse arrays possess inbuilt redundancy to tackle single-element failures. This property enables them to perform accurate direction of arrival (DOA) estimation even during single sensor faults. However, recent literature…
Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of…
Interpretable regression models are important for many application domains, as they allow experts to understand relations between variables from sparse data. Symbolic regression addresses this issue by searching the space of all possible…
Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…
Dynamic symbolic execution (DSE) provides a precise means to analyze programs and it can be used to generate test cases and to detect a variety of bugs including memory vulnerabilities. However, the path explosion problem may prevent a…