arXiv subjects

Aviral Prakash

Publications and source records attributed to Aviral Prakash.

At least 19 recordsLinked to original sources

arXiv2026

GeoQ: Geometry-Aware Conditional Quantile Error Estimation for Scientific Surrogate Models

Neural-network surrogate models are increasingly used to accelerate scientific simulations, but their deployment in extrapolative and autoregressive settings requires input-dependent estimates of prediction error. In this work, we introduce GeoQ (Geometry-Aware Conditional Quantile Error Estimation), a non-intrusive calibration framework for estimating surrogate error at individual query points. GeoQ represents the error at a query point as an anchor-averaged calibration error plus a learned nonnegative correction. This correction is modeled as an upper conditional quantile of the anchor-relative error increment, using geometry-based features that encode representation-space displacement and local support density. A cross-fitting procedure generates approximately out-of-sample calibration tuples, while a feature-space k-nearest-neighbor support score identifies regions \textcolor{black}{where the learned error model is supported by calibration data}. We evaluate GeoQ on scalar regression, chaotic dynamics, medium-range weather forecasting, and Richtmyer-Meshkov instability prediction. The results demonstrate that geometry-aware conditional quantile modeling provides a practical and non-intrusive approach for validity-aware error estimation in scientific surrogate models.

cs.LG↗

arXiv2026

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws

Reduced-order models, such as latent dynamics models, are becoming mainstream for accelerating simulations for parameterized physical systems governed by nonlinear conservation laws. However, most existing latent dynamics frameworks suffer from two important limitations: they do not provide uncertainty estimates for model predictions, and they do not guarantee adherence to the underlying conservation laws. While these challenges have been addressed separately in prior work, a unified framework that simultaneously provides uncertainty quantification and exact conservation-law preservation remains largely unexplored. In this work, we develop a variational latent neural field framework that integrates Gaussian process-inspired surrogates, enabling estimation of predictive confidence for both in-distribution and out-of-distribution parameter regimes. Three variants of the framework are considered: IRS-UQ, PI-IRS-UQ, and ECLEIRS-UQ, corresponding to unconstrained, physics-informed, and conservation-structure-preserving formulations, respectively. Exact conservation-structure preservation is achieved by embedding the solution dynamics within a conservation-law manifold through a space-time divergence-free representation of the solution-flux field. We demonstrate the applicability of the framework through three numerical experiments: 1) 1-D advection, 2) 2-D Euler and 3) 2-D shallow water equations in parameterized settings. Numerical experiments demonstrate that the proposed approach provides accurate predictions together with uncertainty estimates, while remaining robust to sparse and noisy training data. Comparisons between the proposed three approaches show that conservation-structure preserving latent representations improve robustness to degraded training data while maintaining competitive predictive accuracy and uncertainty quantification capability.

physics.comp-ph↗

arXiv2026

Discovery of Sparse Invariant Subgrid-Scale Closures via Dissipation-Controlled Training for Large Eddy Simulation on Anisotropic Grids

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a sparsity-promoting subgrid-scale (SGS) stress closure modeling framework that identifies explicit polynomial model forms using sparse regression. Candidate models are constructed through scaling a minimal tensor basis by a truncated polynomial expansion of invariant scalars, thereby enforcing fundamental invariance properties while regulating the highest order of admissible terms. Arbitrary filter anisotropy is incorporated to enable consistent representation of turbulent structures across computational grids with anisotropic scales and resolutions. We also explicitly constrain SGS energy dissipation during training to improve functional performance and promote numerical stability. The framework is trained on a small dataset of idealized turbulence and evaluated through a series of a priori and a posteriori tests. Sensitivity studies examine the effects of variations in model order and optimization penalties for regularization and dissipation across a range of canonical flow configurations beyond those represented in the training dataset. We also evaluate on a separated flow benchmark to assess generalizability to a more complex turbulent regime. In many cases, the sparse regression closures achieve predictive accuracy comparable to an invariance-preserving neural network while retaining markedly simpler parametric forms. Moreover, we demonstrate that the sparse closures can be trained and evaluated at a fraction of the cost of the neural network model.

physics.flu-dyn↗

arXiv2025

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized partial differential equations from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized PDE systems are expensive due to the high computational cost of high-fidelity simulations. Reduced/Latent state dynamics approaches for parameterized PDEs offer a viable method where high-fidelity data and machine learning techniques are used to reduce the system's dimensionality and estimate the dynamics of low-dimensional reduced states. These reduced state dynamics approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws, especially for parameters that are not a part of the model learning process. In this article, we propose a reduced state dynamics approach, which we refer to as ECLEIRS, that satisfies conservation laws exactly even for parameters unseen in the model training process. ECLEIRS is demonstrated for two applications: 1) obtaining clean solution signals from sparse and noisy measurements of parametric systems, and 2) predicting dynamics for unseen system parameters. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. The numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data. We also demonstrate that ECLEIRS yields solutions and fluxes that satisfy the governing conservation law up to machine precision for unseen parameters, while the other methods yield much higher errors and do not satisfy conservation laws.

physics.comp-ph↗

arXiv2025

General relativistic hydrodynamic simulations of binary strange star mergers

We perform fully general-relativistic simulations of binary strange star mergers considering two different approaches for thermal effects. The first uses a cold equation of state (EOS) derived from a modified version of the MIT bag model which is then supplemented by a $Γ$-law correction. The second approach employs a microphysical description of the finite-temperature effects. We describe results obtained with the two treatments, highlighting the influence of thermal effects. We find that the postmerger dynamics differs significantly in the two cases, leading to quantitative differences in the postmerger gravitational-wave spectrum and ejecta mass. The peak frequency of the postmerger gravitational-wave emission is consistent with the established quasi-universal relations for binary neutron star mergers and as a result, our simulations cannot distinguish between mergers of neutron stars and those of strange stars. Our models with realistic treatment of finite-temperature effects produce a significant amount of ejecta $\gtrsim 0.02\ M_{\odot}$. The resulting flux of strangelets near the Earth, computed assuming that all neutron star mergers are in fact strange-stars mergers and that the binary considered here is representative, is in tension with experimental upper limits. As such, our results tentatively disfavor a scenario in which strange-quark matter is the lowest energy state of matter.

astro-ph.HE↗

arXiv2024

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov-Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through three numerical experiments: 1-D advection equation, 1-D Burgers equation and 2-D advection equation. The results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

physics.comp-ph↗

arXiv2024

SNF-ROM: Projection-based nonlinear reduced order modeling with smooth neural fields

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While commonly used, linear subspace reduced-order models (ROMs) are often suboptimal for problems with a slow decay of Kolmogorov $n$-width, such as advection-dominated fluid flows at high Reynolds numbers. There has been a growing interest in nonlinear ROMs that use state-of-the-art representation learning techniques to accurately capture such phenomena with fewer degrees of freedom. We propose smooth neural field ROM (SNF-ROM), a nonlinear reduced modeling framework that combines grid-free reduced representations with Galerkin projection. The SNF-ROM architecture constrains the learned ROM trajectories to a smoothly varying path, which proves beneficial in the dynamics evaluation when the reduced manifold is traversed in accordance with the governing PDEs. Furthermore, we devise robust regularization schemes to ensure the learned neural fields are smooth and differentiable. This allows us to compute physics-based dynamics of the reduced system nonintrusively with automatic differentiation and evolve the reduced system with classical time-integrators. SNF-ROM leads to fast offline training as well as enhanced accuracy and stability during the online dynamics evaluation. Numerical experiments reveal that SNF-ROM is able to accelerate the full-order computation by up to $199\times$. We demonstrate the efficacy of SNF-ROM on a range of advection-dominated linear and nonlinear PDE problems where we consistently outperform state-of-the-art ROMs.

physics.flu-dyn↗

arXiv2024

Do black holes remember what they are made of?

We study the ringdown signal of black holes formed in prompt-collapse binary neutron star mergers. We analyze data from $47$ numerical relativity simulations. We show that the $(\ell=2,m=2)$ and $(\ell=2,m=1)$ multipoles of the gravitational wave signal are well fitted by decaying damped exponentials, as predicted by black-hole perturbation theory. We show that the ratio of the amplitude in the two modes depends on the progenitor binary mass ratio $q$ and reduced tidal parameter $\tildeΛ$. Unfortunately, the numerical uncertainty in our data is too large to fully quantify this dependency. If confirmed, these results will enable novel tests of general relativity in the presence of matter with next-generation gravitational-wave observatories.

gr-qc↗

arXiv2024

Data-driven identification of stable differential operators using constrained regression

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning sparse differential operators that are theoretically linearly stable by solving a constrained regression problem. These underlying constraints are obtained following linear stability for dynamical systems. We further extend this approach for learning nonlinear differential operators by determining linear stability constraints for linearized equations around an equilibrium point. The applicability of the proposed method is demonstrated for both linear and nonlinear partial differential equations such as 1-D scalar advection-diffusion equation, 1-D Burgers equation and 2-D advection equation. The results indicated that solutions to constrained regression problems with linear stability constraints provide accurate and linearly stable sparse differential operators.

math.NA↗

arXiv2024

Projection-based reduced order modeling and data-driven artificial viscosity closures for incompressible fluid flows

Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the inexpensive online stage. The online stage requires a solution method for the dynamic evolution of the coupled system of pressure and velocity states for incompressible fluid flows. The first contribution of this article is to demonstrate the applicability of the incremental pressure correction scheme for the dynamic evolution of pressure and velocity states. The evolution of a large number of these reduced states in the online stage can be expensive. In contrast, the accuracy significantly decreases if only a few reduced states are considered while not accounting for the interactions between unresolved and resolved states. The second contribution of this article is to compare three closure model forms based on global, modal and tensor artificial viscosity approximation to account for these interactions. The unknown model parameters are determined using two calibration techniques: least squares minimization of error in energy approximation and closure term approximation. This article demonstrates that an appropriate selection of solution methods and data-driven artificial viscosity closure models is essential for consistently accurate dynamics forecasting of incompressible fluid flows.

physics.flu-dyn↗

arXiv2023

Detectability of QCD phase transitions in binary neutron star mergers: Bayesian inference with the next generation gravitational wave detectors

We study the detectability of postmerger QCD phase transitions in neutron star binaries with next-generation gravitational-wave detectors Cosmic Explorer and Einstein Telescope. We perform numerical relativity simulations of neutron star mergers with equations of state that include a quark deconfinement phase transition through either a Gibbs or Maxwell construction. These are followed by Bayesian parameter estimation of the associated gravitational-wave signals using the $\tt{NRPMw}$ waveform model, with priors inferred from the analysis of the inspiral signal. We assess the ability of the model to measure the postmerger peak frequency $f_2^{\rm peak}$ and identify aspects that should be improved in the model. We show that, even at postmerger signal to noise ratios as low as 10, the model can distinguish (at the 90% level) $f_2^{\rm peak}$ between binaries with and without a phase transition in most cases. Phase-transition induced deviations in the $f_2^{\rm peak}$ from the predictions of equation-of-state insensitive relations can also be detected if they exceed $1.6\,\sigma$. Our results suggest that next-generation gravitational wave detectors can measure phase transition effects in binary neutron star mergers. However, unless the phase transition is ``strong'', disentangling it from other hadronic physics uncertainties will require significant theory improvements.

gr-qc↗

arXiv2023

Invariant Data-Driven Subgrid Stress Modeling on Anisotropic Grids for Large Eddy Simulation

We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows using anisotropic grids. The key to our approach is a Galilean, rotationally, reflectionally and unit invariant model form that also embeds filter anisotropy in such a way that an important subgrid stress identity is satisfied. We use this model form to train a data-driven subgrid stress model using only a small amount of anisotropically filtered DNS data and a simple and inexpensive neural network architecture. A priori and a posteriori tests indicate that the trained data-driven model generalizes well to filter anisotropy ratios, Reynolds numbers and flow physics outside the training dataset.

physics.flu-dyn↗

arXiv2023

Thermal Effects in Binary Neutron Star Mergers

We study the impact of finite-temperature effects in numerical-relativity simulations of binary neutron star mergers with microphysical equations of state and neutrino transport in which we vary the effective nucleon masses in a controlled way. We find that, as the specific heat is increased, the merger remnants become colder and more compact due to the reduced thermal pressure support. Using a full Bayesian analysis, we demonstrate that this effect will be measurable in the postmerger gravitational wave signal with next-generation observatories at signal-to-noise ratios of 15.

astro-ph.HE↗

arXiv2023

Turbulent boundary layer with strong favorable pressure gradient and curvature effects: Streamline coordinate and scaling analysis

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favorable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterized and compared to a lower Reynolds number flow over the same geometry. The momentum budgets are analyzed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral analysis-based scalings for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. These proposed scalings exhibit a better collapse of Reynolds stress profiles compared to friction velocity scaling and Zagarola-Smits scaling in the strong favorable pressure gradient region and in the mild adverse pressure region that precedes it in this flow.

physics.flu-dyn↗

arXiv2023

Revealing Phase Transition in Dense Matter with Gravitational Wave Spectroscopy of Binary Neutron Star Mergers

We use numerical relativity simulations of binary neutron star mergers to show that high density deconfinement phase transitions (PTs) to quark matter can be probed using multimodal postmerger gravitational wave (GW) spectroscopy. Hadron-quark PTs suppress the one-armed spiral instability in the remnant. This is manifested in an anti-correlation between the energy carried in the $l=2, m=1$ GW mode and energy density gap which separates the two phases. Consequently, a single measurement of the signal-to-noise ratios of the $l=2, m=1$ and $l=2, m=2$ GW modes could constrain the energy density gap of the PT.

astro-ph.HE↗

arXiv2022

Kilohertz Gravitational Waves From Binary Neutron Star Mergers: Numerical-relativity Informed Postmerger Model

We present ${\tt NRPMw}$, an analytical model of gravitational-waves from neutron star merger remnants informed using 618 numerical relativity (NR) simulations. ${\tt NRPMw}$ is designed in the frequency domain using a combination of complex Gaussian wavelets. The wavelet's parameters are calibrated to equations of state (EOS) insensitive relations from NR data. The NR simulations are computed with 21 EOS (7 of which are finite-temperature microphysical models, and 3 of which contain quark phase transitions or hyperonic degrees of freedom) and span total binary masses $M\in[2.4,3.4]~{\rm M}_\odot$, mass ratios up to $q=2$, and (nonprecessing) dimensionless spins magnitudes up to ${0.2}$. The theoretical uncertainties of the EOS-insensitive relations are incorporated in ${\tt NRPMw}$ using recalibration parameters that enhance the flexibility and accuracy of the model. ${\tt NRPMw}$ is NR-faithful with fitting factors ${\gtrsim}0.9$ computed on an independent validation set of 102 simulations.

gr-qc↗

arXiv2022

Numerical relativity simulations of prompt collapse mergers: threshold mass and phenomenological constraints on neutron star properties after GW170817

We determine the threshold mass for prompt (no bounce) black hole formation in equal-mass neutron star (NS) mergers using a new set of 227 numerical relativity simulations. We consider 23 phenomenological and microphysical finite temperature equations of state (EOS), including models with hyperons and first-order phase transitions to deconfined quarks. We confirm the existence of EOS-insensitive relations between the threshold mass, the binary tidal parameter at the threshold ($Λ_{th}$), the maximum mass of nonrotating NSs, and the radii of reference mass NSs. We correct the systematic errors in previously reported fitting coefficients that were obtained with approximate general-relativity simulations. We combine the EOS-insensitive relations, phenomenological constraints on NS properties and observational data from GW170817 to derive an improved lower limit on radii of maximum mass and 1.6 M$_\odot$ NS of 9.81 km and 10.90 km, respectively. We also constrain the radius and quadrupolar tidal deformability ($Λ$) of a 1.4 $M_\odot$ NS to be larger than 10.74 km and 172, respectively. We consider uncertainties in all independent parameters -- fitting coefficients as well as GW170817 masses while reporting the range of radii constraints. We introduce new methods to constrain the upper as well as lower limit of NS maximum mass using future BNS detections and their identification as prompt or delayed collapse. With future observations it will be possible to derive even tighter constraints on the properties of matter at and above nuclear density using the method proposed in this work.

astro-ph.HE↗

arXiv2022

Optimal Clipping of Structural Subgrid Stress Closures for Large Eddy Simulation

Structural subgrid stress models for large eddy simulation often allow for backscatter of energy from unresolved to resolved turbulent scales, but excessive model backscatter can eventually result in numerical instability. A commonly employed strategy to overcome this issue is to set predicted subgrid stresses to zero in regions of model backscatter. This clipping procedure improves the stability of structural models, however, at the cost of reduced correlation between the predicted subgrid stresses and the exact subgrid stresses. In this article, we propose an alternative strategy that removes model backscatter from model predictions through the solution of a constrained minimization problem. This procedure, which we refer to as optimal clipping, results in a parameter-free mixed model, and it yields predicted subgrid stresses in higher correlation with the exact subgrid stresses as compared with those attained with the traditional clipping procedure. We perform a series of a priori and a posteriori tests to investigate the impact of applying the traditional and optimal clipping procedures to Clark's gradient subgrid stress model, and we observe that optimal clipping leads to a significant improvement in model predictions as compared to the traditional clipping procedure.

physics.flu-dyn↗