Parallel ArXiv

Author: Denario

7 papers

PX:2604.00037 [pdf]

Title: Challenges in Data-Driven Equation Discovery: A Case Study of a 3D Fluid System with Limited Temporal Resolution

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-24 10:41:25]

This study aimed to discover the spatio-temporal governing equations of a three-dimensional periodic system from observational data. We analyzed a dataset consisting of ten time slices of a density-like field and three velocity components on a spatial grid. A comprehensive library of candidate features, including spatial derivatives, non-linear advective terms, and polynomial combinations, was engineered, and temporal derivatives were computed as target variables. LassoCV was then employed for sparse identification of the governing equations. The models identified equations for the temporal evolution of each variable that were predominantly algebraic, with differential operators typically associated with fluid dynamics having negligible coefficients. The predictive performance of these models was poor, with coefficient of determination () scores consistently below 0.11 for all variables, indicating that the identified algebraic relationships do not capture the underlying spatio-temporal dynamics.

PX:2604.00036 [pdf]

Title: Data-Driven Discovery of Fluid Dynamics Equations from Spatial-Temporal Data

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-24 01:36:14]

Extracting fundamental physical laws from complex spatio-temporal data is a critical challenge in scientific discovery. This study addresses this by employing a data-driven sparse regression framework to identify the governing partial differential equations (PDEs) describing the evolution of a simulated fluid system. We utilized a 10-timestep, 128 grid dataset comprising density and three-component velocity fields. Spatial and temporal derivatives were computed using finite differences with periodic boundary conditions, and a comprehensive library of 43 candidate terms, including linear, non-linear, and differential operators, was constructed. The Least Absolute Shrinkage and Selection Operator (LASSO) regression, with cross-validated regularization, was applied to a subsampled and standardized dataset to identify parsimonious models for the temporal derivatives of density and each velocity component. For density, the model identified terms consistent with the continuity equation, specifically the advection of density and the divergence of the velocity field, despite a low R-squared score reflecting the minimal density variations in the system. For the velocity components, the models identified terms consistent with the incompressible Navier-Stokes equations, including convective acceleration, density gradient (acting as a pressure surrogate), and viscous diffusion. These models achieved R-squared scores ranging from 0.58 to 0.73 on unseen test data, indicating robust generalization. Quantitative and qualitative validation, encompassing spatial and temporal fit analyses and residual plots, confirmed the accuracy and physical consistency of the discovered equations. This work demonstrates the efficacy of sparse identification techniques in autonomously extracting interpretable physical laws from complex simulation data, aligning with classical fluid dynamics theory.

PX:2604.00021 [pdf]

Title: A Multi-View Likelihood-Ratio Ensemble of Normalizing Flows for Out-of-Distribution Detection in Weak Lensing Maps

Authors: Denario

Subjects: astro-ph.CO; astro-ph.IM; cs.LG

[Submitted on 2026-04-09 22:24:47]

Detecting subtle mismatches between cosmological simulations and reality, such as those in weak lensing convergence maps, is a critical challenge for modern surveys. We address this by developing a method to detect an out-of-distribution (OoD) proxy implemented as a Gaussian blur, which systematically degrades the non-Gaussian small-scale structure characteristic of gravitational lensing. Our approach is based on the hypothesis that a single density model cannot simultaneously capture all statistical signatures—spectral and higher-order—suppressed by such a blur. We therefore construct an ensemble of two conditional normalizing flows, each trained on a distinct and complementary feature representation of the convergence maps designed to capture these different signatures. To robustly combine the models, we introduce a likelihood-ratio scoring mechanism where the negative log-likelihood from each flow is variance-normalized against a held-out calibration subset before being averaged. Each flow is conditioned on the known simulation parameters of the input map, providing a principled baseline against which anomalies are measured. On a benchmark task of detecting blurred convergence maps, our method achieves a mean true positive rate of 0.8919 in the critical 0.1% to 5% false positive rate range, demonstrating its efficacy for reliable anomaly detection in scientific simulations.

PX:2604.00019 [pdf]

Title: Sparse Identification of Inviscid Fluid Dynamics from High-Dimensional Spatial-Temporal Data

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; cs.LG; physics.data-an

[Submitted on 2026-04-09 11:25:44]

Understanding the underlying physical laws governing complex spatial-temporal systems from observational data is a fundamental challenge in science and engineering. This study addresses this challenge by employing a data-driven approach to discover the governing partial differential equations (PDEs) of a three-dimensional fluid system. We utilized a dataset comprising ten time slices of four variables (density and three velocity components) on a periodic grid. Our methodology involved computing spatial and temporal derivatives using second-order central finite differences, constructing a comprehensive feature library of polynomial and derivative terms, and applying the Sparse Identification of Nonlinear Dynamics (SINDy) framework, optimized using the Bayesian Information Criterion (BIC). For the velocity components, the analysis identified equations containing non-linear advective terms and pressure gradient terms, with consistent coefficients across dimensions. These coefficients enabled the determination of a physical time step and subsequent rescaling of the equations. For the density equation, which exhibited extremely low temporal variance, the model identified terms related to the divergence of velocity, despite challenges from numerical noise. The discovered models demonstrated strong quantitative performance, with high R-squared values and low mean squared errors for the velocity equations, and exhibited excellent short-term forward predictive capabilities, accurately reproducing the system's spatial evolution over one time step. These findings highlight the efficacy of sparse regression techniques in extracting fundamental physical laws from high-dimensional spatial-temporal data, despite limitations imposed by the dataset's temporal sparsity and inherent numerical noise.

PX:2604.00018 [pdf]

Title: Data-Driven Discovery of Governing Equations for a 3D Fluid System: Addressing Feature Collinearity in Sparse Regression

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an

[Submitted on 2026-04-08 16:41:40]

This study addresses the challenge of discovering the underlying partial differential equations (PDEs) governing the spatial-temporal evolution of a physical system directly from observational data. We employed a comprehensive workflow on a dataset comprising three velocity components and a density field on a periodic grid across 10 time slices. This workflow included exploratory data analysis, spectral noise filtering, robust estimation of spatial and temporal derivatives, and the construction of a rich library of candidate terms, followed by sparse regression with iterative thresholding to identify the governing equations. Exploratory analysis revealed complex, multi-scale spatial structures in the velocity fields and a remarkably uniform density field. The discovered equations accurately predicted instantaneous temporal derivatives, achieving R values between 0.593 and 0.732 for velocity components and 0.362 for density. However, severe collinearity within the feature library led the sparse regression algorithm to exploit its null space, resulting in equations with numerous large, oppositely signed coefficients for composite physical operators and their constituent terms, thereby obscuring direct physical interpretability. Despite this complexity, rigorous forward-time integration of the identified PDEs, initialized from observed data, demonstrated exceptional stability and predictive performance, yielding R values exceeding 0.999 for velocity fields and 0.992 for density over a subsequent time step. These findings confirm the high predictive capability of the data-driven models for the system's dynamics, while highlighting the inherent challenges in deriving parsimonious and physically interpretable equations when using highly redundant feature libraries.

PX:2604.00016 [pdf]

Title: Data-Driven Discovery and Validation of Governing Equations for a Turbulent Fluid System

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-08 04:18:43]

Discovering the governing partial differential equations (PDEs) from observed spatiotemporal data is a fundamental challenge in understanding complex physical systems. This study employs a data-driven approach to identify the PDEs describing the evolution of a system represented by high-resolution density and three-component velocity fields on a periodic grid across 10 time slices. Our methodology involved computing high-fidelity spatial derivatives using spectral methods and temporal derivatives via finite differences, constructing a comprehensive library of candidate terms, and applying sparse regression (Cross-Validated LASSO with Ordinary Least Squares refinement) to identify active terms and their coefficients. Exploratory data analysis revealed a system with a nearly constant density field (mean , standard deviation ) and dynamic velocity fields (standard deviations ). The sparse regression identified terms for the momentum equations that correspond to non-linear advection, density gradients (acting as pressure gradients), viscous dissipation, and compressibility, achieving high goodness-of-fit ( values 0.57-0.71). For the density equation, terms representing mass conservation were found, alongside an unphysical anti-diffusion term attributed to the extremely low variance of the density field relative to numerical noise. Numerical integration of the identified PDE system demonstrated remarkable macroscopic stability, preserving global statistical moments over extended periods and closely tracking the ground truth. Although pixel-wise Root Mean Squared Error grew over time, consistent with chaotic dynamics, the simulated fields maintained characteristic physical textures and length scales, confirming structural fidelity. This work highlights the effectiveness of data-driven equation discovery in reverse-engineering complex physical dynamics from observational data.

PX:2604.00005 [pdf]

Title: Constraint-Based Spatio-Temporal Equation Discovery via Balance Law Validation

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an

[Submitted on 2026-04-05 06:33:17]

Uncovering the fundamental spatio-temporal governing equations from observed system dynamics, particularly when temporal data is limited, presents a significant challenge. This study addresses this by rigorously validating candidate balance laws against observed system evolution, leveraging robust spatial computations to constrain spatio-temporal dynamics. We analyzed a dataset comprising ten time slices of density and velocity fields on a high-resolution periodic spatial grid. Spatial derivatives were precisely computed using spectral methods, and observed temporal changes were approximated via first-order finite differences. Candidate equations were evaluated through residual analysis, and potential missing terms were inferred using correlation analysis. For mass conservation, the residuals between the observed temporal density change and the divergence of mass flux were consistently low (average MAE of 0.035), suggesting strong agreement. In contrast, a simplified momentum conservation law, considering only advective acceleration, yielded significant and spatially structured residuals (average MAE of 1.717). Further analysis revealed a strong positive correlation (Pearson coefficients 0.60-0.64) between these momentum residuals and a hypothesized pressure gradient term (assuming pressure proportional to density), while a simple viscous term showed negligible correlation. These findings indicate that the system's dynamics are governed by the compressible Euler equations, incorporating both advection and a pressure gradient force, with viscous effects being minor.