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Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
With the continuous advancement of processors, modern micro-architecture designs have become increasingly complex. The vast design space presents significant challenges for human designers, making design space exploration (DSE) algorithms a…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
Control Flow Graphs are one of the main data sources for software analysis that use dynamic and static software analysis methods. Protected software and modern malware increasingly depend on dynamic code loading techniques to evade static…
Hybrid testing that integrates fuzzing, symbolic execution, and sampling has demonstrated superior testing efficiency compared to individual techniques. However, the state-of-the-art (SOTA) hybrid testing tools do not fully exploit the…
Directed fuzzing is a critical technique in cybersecurity, targeting specific sections of a program. This approach is essential in various security-related domains such as crash reproduction, patch testing, and vulnerability detection.…
A robust observer for performing power system dynamic state estimation (DSE) of a synchronous generator is proposed. The observer is developed using the concept of $\mathcal{L}_{\infty}$ stability for uncertain, nonlinear dynamic generator…
This paper introduces Direct Simplified Symbolic Analysis (DSSA), a new method for simplifying analog circuits. Unlike traditional matrix- or graph-based techniques that are often slow and memory-intensive, DSSA treats the task as a…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
Symbolic execution is a powerful program analysis technique that can formally reason the correctness of program behaviors and detect software bugs. It can systematically explore the execution paths of the tested program. But it suffers from…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
Ensuring that safety-critical applications behave as intended is an important yet challenging task. Modeling languages like differential dynamic logic (dL) have proof calculi capable of proving guarantees for such applications. However, dL…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
This paper presents Mathematical Execution (ME), a new, unified approach for testing numerical code. The key idea is to (1) capture the desired testing objective via a representing function and (2) transform the automated testing problem to…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…