arXiv subjects

R. Rossi

Publications and source records attributed to R. Rossi.

At least 19 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↗

arXiv2024

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

Interaction-enhanced nesting in Spin-Fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the N\'{e}el wave vector, ${\bf Q}_N$, connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from ${\bf Q}_N$ is given by $\chi^{-1} \propto |\Delta q|$. Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a $\chi^{-1} \propto |\Delta q|^{2}$ dependence yields a robust finite-$T$ scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the $(t-t')$ Hubbard model and found that in this case: (i) the FSD is not very pronounced, and, instead, it is the lines of zeros of the renormalized dispersion relation that deform towards nesting; (ii) this phenomenon appears at large $U/t>5.5$ before the formation of electron and hole pockets; (iii) the static spin susceptibility is well described by $\chi^{-1} \propto |\Delta q|^{2}$. Flat FS regions yield a non-trivial scenario for realizing a non-Fermi liquid state.

cond-mat.str-el↗

arXiv2023

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↗

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

Optimization-based Level-Set Re-initialization: A Robust Interface Preserving Approach in Multiphase Problems

In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving the regularity of the distance function. This is mainly due to the stretching (or compressing) effect of the strain rate especially in the vicinity of the liquid-gas interface. Level-set re-initialization is an effective treatment for this issue. However, the traditional approach based on the hyperbolic Hamilton-Jacobi equation is a computationally expensive procedure. Crucially, due to the hyperbolic nature of the formulation, the accuracy of the results hinges significantly on the specialized handling of blind spots near the liquid-gas interface intersecting the substrate. The present work proposes a two-step elliptic level-set re-initialization approach that strictly preserves the location of zero level-set via incorporation of an element splitting process. The primary initialization step helps remove any non-smoothness in the to-be regularized level-set function dramatically improving the efficiency of the secondary optimization step. Geometric representation of the boundary conditions is utilized in the initialization step, while the optimization step minimizes the reliance of the results on the treatment of the blind spots. The performance of the proposed method is examined for free and sessile three-dimensional droplets.

physics.flu-dyn↗

arXiv2023

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↗

arXiv2022

Symmetry-broken perturbation theory to large orders in antiferromagnetic phases

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Phys. Rev. Lett. 119, 045701 (2017)]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the N{\'e}el phase boundary. The critical behavior in its vicinity is shown to be compatible with the $O(3)$ Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at $U/t\!=\!4$. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

cond-mat.str-el↗

arXiv2022

Multiple scattering of channeled and non-channeled positively charged particles in bent monocrystalline silicon

We present the results of an experimental study of multiple scattering of positively charged high energy particles in bent samples of monocrystalline silicon. This work confirms the recently discovered effect of a strong reduction in the rms multiple scattering angle of particles channeled in the silicon (111) plane. The effect is observed in the plane orthogonal to the bending plane. We show in detail the influence of angular constraints on the magnitude of the effect. Comparison of the multiple scattering process at different energies indicates a violation of the law of inverse proportionality of the rms angle of channeled particles with energy. By increasing the statistics, we have improved the results of multiple scattering measurements for particles moving, but not channeled, in silicon crystals.

physics.acc-ph↗

arXiv2021

Double-crystal measurements at the CERN SPS

The UA9 setup, installed in the Super Proton Synchrotron (SPS) at CERN, was exploited for a proof of principle of the double-crystal scenario, proposed to measure the electric and the magnetic moments of short-lived baryons in a high-energy hadron collider, such as the Large Hadron Collider (LHC). Linear and angular actuators were used to position the crystals and establish the required beam configuration. Timepix detectors and high-sensitivity Beam Loss Monitors were exploited to observe the deflected beams. Linear and angular scans allowed exploring the particle interactions with the two crystals and recording their efficiency. The measured values of the beam trajectories, profiles and of the channeling efficiency agree with the results of a Monte-Carlo simulation.

physics.acc-ph↗

arXiv2021

High-order expansion around BCS theory

We demonstrate that summation of connected diagrams to high order starting from a BCS hamiltonian is a viable generic unbiased approach for strongly correlated fermions in superconducting or superfluid phases. For the 3D attractive Hubbard model in a strongly correlated regime, we observe convergence of the diagrammatic series, evaluated up to 12 loops thanks to the connected determinant diagrammatic Monte Carlo algorithm. Our study includes the polarized regime, where conventional quantum Monte Carlo methods suffer from the fermion sign problem. Upon increasing the Zeeman field, we observe the first-order superconducting-to-normal phase transition at low temperature, and a thermally activated polarization of the superconducting phase well described by quasiparticle theory.

cond-mat.str-el↗

arXiv2021

Physical and unphysical regimes of self-consistent many-body perturbation theory

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}\,$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}\,$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}\ $ at small enough coupling, while $G_\infty \neq G_{\rm exact}\ $ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}\ $ and $G_\infty\neq G_{\rm exact}\ $ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\ $, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].

cond-mat.str-el↗

arXiv2020

High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series

We introduce a simple determinant diagrammatic Monte Carlo algorithm to compute the ground-state properties of a particle interacting with a Fermi sea through a zero-range interaction. The fermionic sign does not cause any fundamental problem when going to high diagram orders, and we reach order $N=30$. The data reveal that the diagrammatic series diverges exponentially as $(-1/R)^{N}$ with a radius of convergence $R<1$. Furthermore, on the polaron side of the polaron-dimeron transition, the value of $R$ is determined by a special class of three-body diagrams, corresponding to repeated scattering of the impurity between two particles of the Fermi sea. A power-counting argument explains why finite $R$ is possible for zero-range interactions in three dimensions. Resumming the divergent series through a conformal mapping yields the polaron energy with record accuracy.

cond-mat.quant-gas↗

arXiv2019

Reduction of multiple scattering of high-energy positively charged particles during channeling in single crystals

We present the experimental observation of the reduction of multiple scattering of high-energy positively charged particles during channeling in single crystals. According to our measurements the rms angle of multiple scattering in the plane orthogonal to the plane of the channeling is less than half that for non-channeled particles moving in the same crystal. In the experiment we use focusing bent single crystals. Such crystals have a variable thickness in the direction of beam propagation. This allows us to measure rms angles of scattering as a function of thickness for channeled and non-channeled particles. The behaviour with thickness of non-channeled particles is in agreement with expectations whereas the behaviour of channeled particles has unexpected features. We give a semi-quantitative explanation of the observed effect.

physics.acc-ph↗

arXiv2019

Double-crystal setup measurements at the CERN SPS

In this paper, we discuss an experimental layout for the two-crystals scenario at the Super Proton Synchrotron (SPS) accelerator. The research focuses on a fixed target setup at the circulating machine in a frame of the Physics Beyond Colliders (PBC) project at CERN. The UA9 experiment at the SPS serves as a testbench for the proof of concept, which is planning to be projected onto the Large Hadron Collider (LHC) scale. The presented in the text configuration was used for the quantitative characterization of the deflected particle beam by a pair of bent silicon crystals. For the first time in the double-crystal configuration, a particle deflection efficiency by the second crystal of $0.188 \pm 3 \cdot 10^{-5}$ and $0.179 \pm 0.013$ was measured on the accelerator by means of the Timepix detector and Beam Loss Monitor (BLM) respectively. In this setup, a wide range angular scan allowed a possibility to \textit{in situ} investigate different crystal working regimes (channeling, volume reflection, etc.), and to measure a bent crystal torsion.

physics.acc-ph↗

arXiv2019

Commissioning and operation of the Cherenkov detector for proton Flux Measurement of the UA9 Experiment

The UA9 Experiment at CERN-SPS investigates channeling processes in bent silicon crystals with the aim to manipulate hadron beams. Monitoring and characterization of channeled beams in the high energy accelerators environment ideally requires in-vacuum and radiation hard detectors. For this purpose the Cherenkov detector for proton Flux Measurement (CpFM) was designed and developed. It is based on thin fused silica bars in the beam pipe vacuum which intercept charged particles and generate Cherenkov light. The first version of the CpFM is installed since 2015 in the crystal-assisted collimation setup of the UA9 experiment. In this paper the procedures to make the detector operational and fully integrated in the UA9 setup are described. The most important standard operations of the detector are presented. They have been used to commission and characterize the detector, providing moreover the measurement of the integrated channeled beam profile and several functionality tests as the determination of the crystal bending angle. The calibration has been performed with Lead (Pb) and Xenon (Xe) beams and the results are applied to the flux measurement discussed here in detail.

physics.ins-det↗

arXiv2018

Contact and Momentum Distribution of the Unitary Fermi Gas

A key quantity in strongly-interacting resonant Fermi gases is the contact $\mathcal{C}$, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of $\mathcal{C}$ was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by Bold Diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.

cond-mat.quant-gas↗

arXiv2017

Experimental results of crystal-assisted slow extraction at the SPS

The possibility of extracting highly energetic particles from the Super Proton Synchrotron (SPS) by means of silicon bent crystals has been explored since the 1990's. The channelling effect of a bent crystal can be used to strongly deflect primary protons and eject them from the synchrotron. Many studies and experiments have been carried out to investigate crystal channelling effects. The extraction of 120 and 270 GeV proton beams has already been demonstrated in the SPS with dedicated experiments located in the ring. Presently in the SPS, the UA9 experiment is performing studies to evaluate the possibility to use bent silicon crystals to steer particle beams in high energy accelerators. Recent studies on the feasibility of extraction from the SPS have been made using the UA9 infrastructure with a longer-term view of using crystals to help mitigate slow extraction induced activation of the SPS. In this paper, the possibility to eject particles into the extraction channel in LSS2 using the bent crystals already installed in the SPS is presented. Details of the concept, simulations and measurements carried out with beam are presented, before the outlook for the future is discussed.

physics.acc-ph↗