arXiv subjects

Federico J. Gonzalez

Publications and source records attributed to Federico J. Gonzalez.

4 recordsLinked to original sources

arXiv2026

PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability

Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements. A known issue is the ill-conditioned nature of the inverse problem, which frequently produces multiple mathematical models that fit the data similarly well. One path to address this issue is by incorporating known hypotheses and constraints into the training phase beforehand. While this approach effectively reduces the search space, it still results in multiple candidate models, forcing practitioners to rely on post-hoc manual filtering based on their own domain expertise. A recent approach incorporates structural `skeletons' inspired by characteristic curves (CCs), defining a hypothesis-driven methodology. In this methodology, practitioners define a skeleton, which is associated with a family of ordinary differential equations (ODEs), and then add their hypotheses and priors based on their domain knowledge to refine the obtained model iteratively. An important advantage of this approach is that some skeletons have demonstrable structural identifiability properties, which are useful for checking whether the skeleton is correct or should be discarded. Furthermore, this formalism enables the use of multiple equation discovery paradigms due to its modularity (such as neural networks, symbolic regression, and sparse regression). In this work, we present the Python library PyCC, which condenses these efforts into a flexible tool that allows researchers and engineers to seamlessly define their skeletons and hypotheses to discover ODEs from time-dependent data.

cs.LG↗

arXiv2026

Integrating prior knowledge in equation discovery: Interpretable symmetry-informed neural networks and symbolic regression via characteristic curves

Data-driven equation discovery aims to reconstruct governing equations directly from empirical observations. A fundamental challenge in this domain is the ill-posed nature of the inverse problem, where multiple distinct mathematical models may yield similar errors, thus complicating model selection and failing to guarantee a unique representation of the underlying mechanisms. This issue can be addressed by incorporating inductive biases to constrain the search space and discard the undesirable models. The characteristic curves-based (CCs) framework offers a modular approach ideally suited to this aim. This approach is based on the specification of structural families that possess provable identifiability properties. Crucially, this framework enables practitioners to embed domain expertise directly into the learning process and facilitates the integration of diverse post-processing tools. In this work, we build upon the recent neural network implementation of this formalism (NN-CC), which benefits from the universal approximation capabilities of NNs. Specifically, we extend NN-CC by introducing two inductive biases: (i) symmetry constraints and (ii) post-processing with symbolic regression. Using a chaotic Duffing oscillator and a discontinuous stick-slip model under varying Gaussian noise levels, we show how these extensions systematically improve the discovery process. We also analyze the integration of sparse and symbolic regression (using SINDy and PySR) into the CC-based formalism. These extensions (SINDy-CC and SR-CC) consistently show improvements as prior information is incorporated. By enabling the integration of prior or hypothesized knowledge into the learning and post-processing stages, the CC-based formalism emerges as a promising candidate to address identifiability issues in purely data-driven methods, advancing the goal of interpretable and reliable system identification.

nlin.CD↗

arXiv2025

CO$_2$ Dissociative Sticking on Cu(110)

In this work we investigate the dissociation of CO$_2$ on Cu(110) by performing density functional theory calculations using the vdW-DF2 exchange-correlation functional, with a potential energy surface parameterized using artificial neural networks. We computed quasi-classical trajectory calculations of molecular and dissociative adsorption probabilities as a function of the initial impact energy of the molecules and surface temperature, by comparing our results with available supersonic molecular beam experimental data for normal incidence. Concerning the general dependence of the molecular and dissociative adsorption probabilities on the initial translational energy of the molecules, our theoretical results agree with experiments. Also in agreement with experiments, we have found that dissociative adsorption is not affected by surface temperature between 50 and 400 K, for impact energies for which the dissociation probability is larger than $\sim 10^{-3}$. We have investigated the influence of impact energy and surface temperature on the final state of the dissociation products by extending the time integration of the reactive trajectories up to 10 ps. We have found that above $\sim 2.5$ eV and close to or above room temperature, CO$_2$ dissociation induces strong surface distortions including final structures involving Cu adatoms. The creation of Cu vacancy-adatom pairs is stimulated by the presence of both CO$_{ads}$ and O$_{ads}$ which interact strongly with the Cu adatoms and even give rise to unexpected (O-Cu-CO)$_{ads}$ linear moieties anchored to the surface by the dissociated O atom and involving a Cu adatom almost detached from the surface. These surface distortions produced by dissociation products of high energy CO$_2$ molecules at and above room temperature might explain recent experiments that have found a greater saturation oxygen coverage for high energy molecules.

cond-mat.mtrl-sci↗

arXiv2025

Interpretable neural network system identification method for two families of second-order systems based on characteristic curves

Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the mathematical structure of the governing differential equations with the flexibility of neural networks (NNs). At the core of our approach is the concept of characteristic curves (CCs), which represent individual nonlinear functions (e.g., friction and restoring components) of the system. Each CC is modeled by a dedicated NN, enabling a modular and interpretable representation of the system equation. To demonstrate the versatility of the CC-based formalism, we introduce three identification strategies: (1) SINDy-CC, which extends the sparse regression approach of SINDy by incorporating the mathematical structure of the governing equations as constraints; (2) Poly-CC, which represents each CC using high-degree polynomials; and (3) NN-CC, which uses NNs without requiring prior assumptions about basis functions. Our results show that all three approaches are well-suited for systems with simple polynomial nonlinearities, such as the van der Pol oscillator. In contrast, NN-CC demonstrates superior performance in modeling systems with complex nonlinearities and discontinuities, such as those observed in stick-slip systems. The key contribution of this work is to demonstrate that the CC-based framework, particularly the NN-CC approach, can capture complex nonlinearities while maintaining interpretability through the explicit representation of the CCs. This balance makes it well-suited for modeling systems with discontinuities and complex nonlinearities that are challenging to assess using traditional polynomial or sparse regression methods, providing a powerful tool for nonlinear system identification.

cs.LG↗