arXiv subjects

J. R. Bravo

Publications and source records attributed to J. R. Bravo.

7 recordsLinked to original sources

arXiv2025

A discrete physics-informed training for projection-based reduced order models with neural networks

This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Key contributions include: (1) a parameter-agnostic, discrete residual loss applicable to non-linear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics informed training process for ROMs. The method is demonstrated on a non-linear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on non-linear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use-case. Finally, the application of physics informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy, however it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN.

cs.LG↗

arXiv2025

Parallel Reduced Order Modeling for Digital Twins using High-Performance Computing Workflows

The integration of reduced-order models (ROMs) with high-performance computing (HPC) is critical for developing digital twins, particularly for real-time monitoring and predictive maintenance of industrial systems. This paper presents a comprehensive, HPC-enabled workflow for developing and deploying projection-based reduced-order models (PROMs) for large-scale mechanical simulations. We use PyCOMPSs' parallel framework to efficiently execute ROM training simulations, employing parallel singular value decomposition (SVD) algorithms such as randomized SVD, Lanczos SVD, and full SVD based on tall-skinny QR (TSQR). Moreover, we introduce a partitioned version of the hyper-reduction scheme known as the Empirical Cubature Method (ECM) to further enhance computational efficiency in PROMs for mechanical systems. Despite the widespread use of HPC for PROMs, there is a significant lack of publications detailing comprehensive workflows for building and deploying end-to-end PROMs in HPC environments. Our workflow is validated through a case study focusing on the thermal dynamics of a motor, a multiphysics problem involving convective heat transfer and mechanical components. The PROM is designed to deliver a real-time prognosis tool that could enable rapid and safe motor restarts post-emergency shutdowns under different operating conditions, demonstrating its potential impact on the practice of simulations in engineering mechanics. To facilitate deployment, we use the Workflow as a Service (WaaS) strategy and Functional Mock-Up Units (FMUs) to ensure compatibility and ease of integration across HPC, edge, and cloud environments. The outcomes illustrate the efficacy of combining PROMs and HPC, establishing a precedent for scalable, real-time digital twin applications in computational mechanics across multiple industries.

cs.DC↗

arXiv2024

A subspace-adaptive weights cubature method with application to the local hyperreduction of parameterized finite element models

This paper is concerned with quadrature/cubature rules able to deal with multiple subspaces of functions, in such a way that the integration points are common for all the subspaces, yet the weights are tailored to each specific subspace. These subspace-adaptive weights cubature rules can be used to accelerate computational mechanics applications requiring efficiently evaluating spatial integrals whose integrand function dynamically switches between multiple pre-computed subspaces. One of such applications is local hyperreduced-order modeling (HROM), in which the solution manifold is approximately represented as a collection of basis matrices, each basis matrix corresponding to a different region in parameter space. We pose the optimization problem and propose two algorithms for its resolution. The first one is a greedy strategy based on an enhanced version of the Empirical Cubature Method (ECM) developed by the authors elsewhere (we call it the Subspace-Adaptive Weights ECM, SAW-ECM for short), while the second method is based on a convexification of the cubature problem so that it can be addressed by linear programming algorithms. We show in a toy problem involving integration of polynomial functions that the SAW-ECM clearly outperforms the other method both in terms of computational cost and optimality. We illustrate the performance of the SAW-ECM in the construction of a local HROMs in a highly nonlinear equilibrium problem (large strains regime). We demonstrate that, provided that the subspace-transition errors are negligible, the error associated to hyperreduction using adaptive weights can be controlled by the truncation tolerances of the SVDs used for determining the basis matrices. The Python source codes of the proposed SAW-ECM are openly accessible in the public repository https://github.com/Rbravo555/localECM.

math-ph↗

arXiv2024

Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behavior of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution. The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behavior in a phase-space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI. While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

physics.flu-dyn↗

arXiv2023

Hyper-reduction for Petrov-Galerkin reduced order models

Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is optimally achieved by projecting the full order residual onto the approximation basis (Galerkin Projection). This is sub-optimal for non-SPD Jacobians as it only minimizes the projection of the residual, not the residual itself. An alternative is to directly minimize the 2-norm of the residual, achievable using QR factorization or the method of the normal equations (LSPG). The first approach involves constructing and factorizing a large matrix, while LSPG avoids this but requires constructing a product element by element, necessitating a complementary mesh and adding complexity to the hyper-reduction process. This work proposes an alternative based on Petrov-Galerkin minimization. We choose a left basis for a least-squares minimization on a reduced problem, ensuring the discrete full order residual is minimized. This is applicable to both SPD and non-SPD Jacobians, allowing element-by-element assembly, avoiding the use of a complementary mesh, and simplifying finite element implementation. The technique is suitable for hyper-reduction using the Empirical Cubature Method and is applicable in nonlinear reduction procedures.

cs.CE↗

arXiv2023

CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models

We present the Continuous Empirical Cubature Method (CECM), a novel algorithm for empirically devising efficient integration rules. The CECM aims to improve existing cubature methods by producing rules that are close to the optimal, featuring far less points than the number of functions to integrate. The CECM consists on a two-stage strategy. First, a point selection strategy is applied for obtaining an initial approximation to the cubature rule, featuring as many points as functions to integrate. The second stage consists in a sparsification strategy in which, alongside the indexes and corresponding weights, the spatial coordinates of the points are also considered as design variables. The positions of the initially selected points are changed to render their associated weights to zero, and in this way, the minimum number of points is achieved. Although originally conceived within the framework of hyper-reduced order models (HROMs), we present the method's formulation in terms of generic vector-valued functions, thereby accentuating its versatility across various problem domains. To demonstrate the extensive applicability of the method, we conduct numerical validations using univariate and multivariate Lagrange polynomials. In these cases, we show the method's capacity to retrieve the optimal Gaussian rule. We also asses the method for an arbitrary exponential-sinusoidal function in a 3D domain, and finally consider an example of the application of the method to the hyperreduction of a multiscale finite element model, showcasing notable computational performance gains. A secondary contribution of the current paper is the Sequential Randomized SVD (SRSVD) approach for computing the Singular Value Decomposition (SVD) in a column-partitioned format. The SRSVD is particularly advantageous when matrix sizes approach memory limitations.

math.NA↗

arXiv2017

Early Spectra of the Gravitational Wave Source GW170817: Evolution of a Neutron Star Merger

On 2017 August 17, Swope Supernova Survey 2017a (SSS17a) was discovered as the optical counterpart of the binary neutron star gravitational wave event GW170817. We report time-series spectroscopy of SSS17a from 11.75 hours until 8.5 days after merger. Over the first hour of observations the ejecta rapidly expanded and cooled. Applying blackbody fits to the spectra, we measure the photosphere cooling from $11,000^{+3400}_{-900}$ K to $9300^{+300}_{-300}$ K, and determine a photospheric velocity of roughly 30% of the speed of light. The spectra of SSS17a begin displaying broad features after 1.46 days, and evolve qualitatively over each subsequent day, with distinct blue (early-time) and red (late-time) components. The late-time component is consistent with theoretical models of r-process-enriched neutron star ejecta, whereas the blue component requires high velocity, lanthanide-free material.

astro-ph.HE↗