Related papers: Symbolic-numeric methods for improving structural …
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Recent work on Neural-Symbolic systems that learn the discrete planning model from images has opened a promising direction for expanding the scope of Automated Planning and Scheduling to the raw, noisy data. However, previous work only…
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.…
System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…
[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…
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…
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…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional…
Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test…
We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and…
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular…
Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…
The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…