Related papers: A Tutorial on Symbolic Structural Identifiability …
Integro-differential-algebraic equations (IDAE)s are widely used in applications of engineering and analysis. When there are hidden constraints in an IDAE, structural analysis is necessary. But if derivatives of dependent variables appear…
In this paper, we introduce a new identifiability criteria for linear structural equation models, which we call regression identifiability. We provide necessary and sufficient graphical conditions for a directed edge to be regression…
Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to…
Flow diagrams are a common tool used to help build and interpret models of dynamical systems, often in biological contexts such as consumer-resource models and similar compartmental models. Typically, their usage is intuitive and informal.…
Conceptual hydrologic models remain the cornerstone of rainfall-runoff modeling, yet their calibration is often slow and numerically fragile. Most gradient-based parameter estimation methods rely on finite-difference approximations or…
Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming…
Copulas are functions that describe dependence structures of random vectors, without describing their univariate marginals. In statistics, the separation is sometimes useful, the quality and/or quantity of available information on these two…
The n body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learning models that are used for predicting and forecasting…
Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not…
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
Labeling neural network submodules with human-legible descriptions is useful for many downstream tasks: such descriptions can surface failures, guide interventions, and perhaps even explain important model behaviors. To date, most…
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…
Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional…
Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…
A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE)…
The MRI-derived brain network serves as a pivotal instrument in elucidating both the structural and functional aspects of the brain, encompassing the ramifications of diseases and developmental processes. However, prevailing methodologies,…
There has been a growing interest in extracting formal descriptions of the system behaviors from data. Signal Temporal Logic (STL) is an expressive formal language used to describe spatial-temporal properties with interpretability. This…
Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…