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In this paper the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterization of…
Dual encoders have been used for question-answering (QA) and information retrieval (IR) tasks with good results. Previous research focuses on two major types of dual encoders, Siamese Dual Encoder (SDE), with parameters shared across two…
A new causal discovery method, Structural Agnostic Modeling (SAM), is presented in this paper. Leveraging both conditional independencies and distributional asymmetries, SAM aims to find the underlying causal structure from observational…
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…
Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the…
Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses. However, the PDEs of many…
A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations.…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
Traditional machine learning assumes that training and test sets are derived from the same distribution; however, this assumption does not always hold in practical applications. This distribution disparity can lead to severe performance…
We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a nonlinear…
Typically, a practical algorithm of hardware verification obtains a semantic result by being applied to a particular formula $F$. That is, although this algorithm uses the specifics of $F$ (sometimes inadvertently), its result holds for all…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a…
We consider the large scale nonsymmetric algebraic Riccati equation arising in transport theory, where the $n\times n$ coefficient matrices $B, C$ are symmetric and low-ranked and $A, E$ are rank one updates of nonsingular diagonal…
Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems…
Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…