arXiv subjects

Spencer H. Bryngelson

Publications and source records attributed to Spencer H. Bryngelson.

At least 37 records · Page 2Linked to original sources

arXiv2025

Accelerating Bayesian Optimal Experimental Design via Local Radial Basis Functions: Application to Soft Material Characterization

We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The presented RBF--BOED method uses the intrinsic ability of RBFs to handle scattered parameter points, a property that aligns naturally with the probabilistic sampling inherent in Bayesian methods. By constructing accurate deterministic surrogates from local neighborhood information, the method enables high-order approximations with reduced computational overhead. As a result, computing the expected information gain (EIG) requires evaluating only a small uniformly sampled subset of prior parameter values, greatly reducing the number of expensive forward-model simulations needed. For demonstration, we apply RBF--BOED to optimize a laser-induced cavitation (LIC) experimental setup, where forward simulations follow from inertial microcavitation rheometry (IMR) and characterize the viscoelastic properties of hydrogels. Two experimental design scenarios, single- and multi-constitutive-model problems, are explored. Results show that EIG estimates can be obtained at just 8% of the full computational cost in a five-model problem within a two-dimensional design space. This advance offers a scalable path toward optimal experimental design in soft and biological materials.

physics.comp-ph↗

arXiv2025

Pyrometheus: Symbolic abstractions for XPU and automatically differentiated computation of combustion kinetics and thermodynamics

The cost of combustion simulations is often dominated by the evaluation of net production rates of chemical species and mixture thermodynamics (thermochemistry). Execution on computing accelerators (XPUs) like graphic processing units (GPUs) can greatly reduce this cost. However, established thermochemistry software is not readily portable to such devices or sacrifices valuable analytical forms that enable differentiation for sensitivity analysis and implicit time integration. Symbolic abstractions are developed with corresponding transformations that enable computation on accelerators and automatic differentiation by avoiding premature specification of detail. The software package Pyrometheus is introduced as an implementation of these abstractions and their transformations for combustion thermochemistry. The formulation facilitates code generation from the symbolic representation of a specific thermochemical mechanism in multiple target languages, including Python, C++, and Fortran. Computational concerns are separated: the generated code processes array-valued expressions but does not specify their semantics. These semantics are provided by compatible array libraries, such as NumPy, Pytato, and Google JAX. Thus, the generated code retains a symbolic representation of the thermochemistry, which translates to computation on accelerators and CPUs and automatic differentiation. The design and operation of these symbolic abstractions and their companion tool, Pyrometheus, are discussed throughout. Roofline demonstrations show that the computation of chemical source terms within MFC, a Fortran-based flow solver we link to Pyrometheus, is performant.

physics.comp-ph↗

arXiv2025

Parsimonious inertial cavitation rheometry via bubble collapse time

The rapid and accurate characterization of soft, viscoelastic materials at high strain rates is of interest in biological and engineering applications. Examples include assessing the extent of tissue ablation during histotripsy procedures and developing injury criteria for the mitigation of blast injuries. The inertial microcavitation rheometry technique (IMR, Estrada et al., 2018) allows for the characterization of local viscoelastic properties at strain rates up to 1E8 per second. However, IMR now typically relies on bright-field videography of a sufficiently translucent sample at >1 million frames per second and a simulation-dependent fit optimization process that can require hours of post-processing. Here, we present an improved IMR-style technique, called parsimonious inertial microcavitation rheometry (pIMR), that parsimoniously characterizes surrounding viscoelastic materials. The pIMR approach uses experimental advancements to estimate the time to first collapse of the laser-induced cavity within approximately 20 ns and a theoretical energy balance analysis that yields an approximate collapse time based on the material viscoelasticity parameters. The pIMR method closely matches the accuracy of the original IMR procedure while decreasing the computational cost from hours to seconds while potentially reducing reliance on ultra-high-speed videography. This technique can enable nearly real-time characterization of soft, viscoelastic hydrogels and biological materials with a numerical criterion assessing the correct choice of model. We illustrate the efficacy of the technique on batches of tens of experiments for both soft hydrogels and fluids.

cond-mat.soft↗

arXiv2024

A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method

This work proposes a multi-circuit quantum lattice Boltzmann method (QLBM) algorithm that leverages parallel quantum computing to reduce quantum resource requirements. Computational fluid dynamics (CFD) simulations often entail a large computational burden on classical computers. At present, these simulations can require up to trillions of grid points and millions of time steps. To reduce costs, novel architectures like quantum computers may be intrinsically more efficient for these computations. Current quantum algorithms for solving CFD problems are based on single quantum circuits and, in many cases, use lattice-based methods. Current quantum devices are adorned with sufficient noise to make large and deep circuits untenable. We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations. The method, called QLBM-frugal, aims to create more practical quantum circuits and strategies for differential equation-based problems. The presented method is validated and demonstrated for 2D lid-driven cavity flow. The two-circuit algorithm shows a marked reduction in CNOT gates, which consume the majority of the runtime on quantum devices. Compared to the baseline QLBM technique, a two-circuit strategy shows increasingly large improvements in gate counts as the qubit size, or problem size, increases. For 64 lattice sites, the CNOT count was reduced by 35%, and the gate depth decreased by 16%. This strategy also enables concurrent circuit execution, further halving the seen gate depth.

quant-ph↗

arXiv2024

Bayesian optimal design accelerates discovery of material properties from bubble dynamics

An optimal sequential experimental design approach is developed to computationally characterize soft material properties at the high strain rates associated with bubble cavitation. The approach involves optimal design and model inference. The optimal design strategy maximizes the expected information gain in a Bayesian statistical setting to design experiments that provide the most informative cavitation data about unknown soft material properties. We infer constitutive models by characterizing the associated viscoelastic properties from measurements via a hybrid ensemble-based 4D-Var method (En4D-Var). The inertial microcavitation-based high strain-rate rheometry (IMR) method ([1]) simulates the bubble dynamics under laser-induced cavitation. We use experimental measurements to create synthetic data representing the viscoelastic behavior of stiff and soft polyacrylamide hydrogels under realistic uncertainties. The synthetic data are seeded with larger errors than state-of-the-art measurements yet match known material properties, reaching 1% relative error within 10 sequential designs (experiments). We discern between two seemingly equally plausible constitutive models, Neo-Hookean Kelvin--Voigt and quadratic Kelvin--Voigt, with a probability of correctness larger than 99% in the same number of experiments. This strategy discovers soft material properties, including discriminating between constitutive models and discerning their parameters, using only a few experiments.

cond-mat.soft↗

arXiv2024

Incompressible Navier-Stokes solve on noisy quantum hardware via a hybrid quantum-classical scheme

Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable exponential speedups over algorithms on classical computers. However, current and foreseeable quantum hardware introduce noise into computations, requiring algorithms that make judicious use of quantum resources: shallower circuit depths and fewer qubits. Under these restrictions, variational algorithms are more appropriate and robust. This work presents a hybrid quantum-classical algorithm for the incompressible Navier--Stokes equations. A classical device performs nonlinear computations, and a quantum one uses a variational solver for the pressure Poisson equation. A lid-driven cavity problem benchmarks the method. We verify the algorithm via noise-free simulation and test it on noisy IBM superconducting quantum hardware. Results show that high-fidelity results can be achieved via this approach, even on current quantum devices. Multigrid preconditioning of the Poisson problem helps avoid local minima and reduces resource requirements for the quantum device. A quantum state readout technique called HTree is used for the first time on a physical problem. Htree is appropriate for real-valued problems and achieves linear complexity in the qubit count, making the Navier-Stokes solve further tractable on current quantum devices. We compare the quantum resources required for near-term and fault-tolerant solvers to determine quantum hardware requirements for fluid simulations with complexity improvements.

physics.flu-dyn↗

arXiv2024

OpenACC offloading of the MFC compressible multiphase flow solver on AMD and NVIDIA GPUs

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses 'gang vector' and 'collapse'. Further speedups of six and ten times are achieved by packing user-defined types into coalesced multidimensional arrays and manual inlining via metaprogramming. Additional optimizations yield seven-times speedup in array packing and thirty-times speedup of select kernels on Frontier. Weak scaling efficiencies of 97% and 95% are observed when scaling to 50% of Summit and 95% of Frontier. Strong scaling efficiencies of 84% and 81% are observed when increasing the device count by a factor of 8 and 16 on V100 and MI250X hardware. The strong scaling efficiency of AMD's MI250X increases to 92% when increasing the device count by a factor of 16 when GPU-aware MPI is used for communication.

physics.flu-dyn↗

arXiv2024

Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme

Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness of the solution, dynamically adapting the stencil weights based on local solution features. As rational neural networks can represent fast transitions between smooth and sharp regimes, this approach achieves a granular reconstruction with significantly reduced dissipation, improving the accuracy of the simulation. The network is trained offline on a carefully chosen dataset of analytical functions, bypassing the need for differentiable solvers. We also propose a robust model selection criterion based on estimates of the interpolation's convergence order on a set of test functions, which correlates better with the model performance in downstream tasks. We demonstrate the effectiveness of our approach on several one-, two-, and three-dimensional fluid flow problems: our scheme generalizes across grid resolutions while handling smooth and discontinuous solutions. In most cases, our rational network-based scheme achieves higher accuracy than conventional WENO3 with the same stencil size, and in a few of them, it achieves accuracy comparable to WENO5, which uses a larger stencil.

math.NA↗

arXiv2024

Fully quantum algorithm for lattice Boltzmann methods with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. This method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical PDEs: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

physics.comp-ph↗

arXiv2024

Neural networks can be FLOP-efficient integrators of 1D oscillatory integrands

We demonstrate that neural networks can be FLOP-efficient integrators of one-dimensional oscillatory integrands. We train a feed-forward neural network to compute integrals of highly oscillatory 1D functions. The training set is a parametric combination of functions with varying characters and oscillatory behavior degrees. Numerical examples show that these networks are FLOP-efficient for sufficiently oscillatory integrands with an average FLOP gain of 1000 FLOPs. The network calculates oscillatory integrals better than traditional quadrature methods under the same computational budget or number of floating point operations. We find that feed-forward networks of 5 hidden layers are satisfactory for a relative accuracy of 0.001. The computational burden of inference of the neural network is relatively small, even compared to inner-product pattern quadrature rules. We postulate that our result follows from learning latent patterns in the oscillatory integrands that are otherwise opaque to traditional numerical integrators.

cs.LG↗

arXiv2024

Method for portable, scalable, and performant GPU-accelerated simulation of multiphase compressible flow

Multiphase compressible flows are often characterized by a broad range of space and time scales. Thus entailing large grids and small time steps, simulations of these flows on CPU-based clusters can thus take several wall-clock days. Offloading the compute kernels to GPUs appears attractive but is memory-bound for standard finite-volume and -difference methods, damping speed-ups. Even when realized, faster GPU-based kernels lead to more intrusive communication and I/O times. We present a portable strategy for GPU acceleration of multiphase compressible flow solvers that addresses these challenges and obtains large speedups at scale. We use OpenACC for portable offloading of all compute kernels while maintaining low-level control when needed. An established Fortran preprocessor and metaprogramming tool, Fypp, enables otherwise hidden compile-time optimizations. This strategy exposes compile-time optimizations and high memory reuse while retaining readable, maintainable, and compact code. Remote direct memory access, realized via CUDA-aware MPI, reduces communication times. We implement this approach in the open-source solver MFC. Metaprogramming-based preprocessing results in an 8-times speedup of the most expensive kernels, 46% of peak FLOPs on NVIDIA GPUs, and high arithmetic intensity (about 10 FLOPs/byte). In representative simulations, a single A100 GPU is 300-times faster than an Intel Xeon CPU core, corresponding to a 9-times speedup for a single A100 compared to the entire CPU die. At the same time, near-ideal (97%) weak scaling is observed for at least 13824 GPUs on Summit. A strong scaling efficiency of 84% is retained for an 8-times increase in GPU count. Collective I/O, implemented via MPI3, helps ensure negligible contribution of data transfers. Large many-GPU simulations of compressible (solid-)liquid-gas flows demonstrate the practical utility of this strategy.

physics.flu-dyn↗

arXiv2023

Targeted computation of nonlocal closure operators via an adjoint-based macroscopic forcing method

Reynolds-averaged Navier--Stokes (RANS) closure must be sensitive to the flow physics, including nonlocality and anisotropy of the effective eddy viscosity. Recent approaches used forced direct numerical simulations to probe these effects, including the macroscopic forcing method (MFM) of Mani and Park ($\textit{Phys. Rev. Fluids}$ $\textbf{6}$, 054607 (2021)) and the Green's function approach of Hamba ($\textit{Phys. Fluids}$ $\textbf{17}$, 115102 (2005)). The resulting nonlocal and anisotropic eddy viscosities are exact and relate Reynolds stresses to mean velocity gradients at all locations. They can be used to inform RANS models of the sensitivity to the mean velocity gradient and the suitability of local and isotropic approximations. However, these brute-force approaches are expensive. They force the mean velocity gradient at each point in the averaged space and measure the Reynolds stress response, requiring a separate simulation for each mean velocity gradient location. Thus, computing the eddy viscosity requires as many simulations as degrees of freedom in the averaged space, which can be cost-prohibitive for problems with many degrees of freedom. In this work, we develop an adjoint-based MFM to obtain the eddy viscosity at a given Reynolds stress location using a single simulation. This approach recovers the Reynolds stress dependence at a location of interest, such as a separation point or near a wall, on the mean velocity gradient at all locations. We demonstrate using adjoint MFM to compute the eddy viscosity for a specified wall-normal location in an incompressible turbulent channel flow using one simulation. In contrast, a brute-force approach for the same problem requires $N=144$ simulations (the number of grid points in the non-averaged coordinate direction). We show that a local approximation for the eddy viscosity would have been inappropriate.

physics.flu-dyn↗

arXiv2023

RoseNNa: A performant, portable library for neural network inference with application to computational fluid dynamics

The rise of neural network-based machine learning ushered in high-level libraries, including TensorFlow and PyTorch, to support their functionality. Computational fluid dynamics (CFD) researchers have benefited from this trend and produced powerful neural networks that promise shorter simulation times. For example, multilayer perceptrons (MLPs) and Long Short Term Memory (LSTM) recurrent-based (RNN) architectures can represent sub-grid physical effects, like turbulence. Implementing neural networks in CFD solvers is challenging because the programming languages used for machine learning and CFD are mostly non-overlapping, We present the roseNNa library, which bridges the gap between neural network inference and CFD. RoseNNa is a non-invasive, lightweight (1000 lines), and performant tool for neural network inference, with focus on the smaller networks used to augment PDE solvers, like those of CFD, which are typically written in C/C++ or Fortran. RoseNNa accomplishes this by automatically converting trained models from typical neural network training packages into a high-performance Fortran library with C and Fortran APIs. This reduces the effort needed to access trained neural networks and maintains performance in the PDE solvers that CFD researchers build and rely upon. Results show that RoseNNa reliably outperforms PyTorch (Python) and libtorch (C++) on MLPs and LSTM RNNs with less than 100 hidden layers and 100 neurons per layer, even after removing the overhead cost of API calls. Speedups range from a factor of about 10 and 2 faster than these established libraries for the smaller and larger ends of the neural network size ranges tested.

physics.flu-dyn↗

arXiv2023

Fast Macroscopic Forcing Method

The macroscopic forcing method (MFM) of Mani and Park and similar methods for obtaining turbulence closure operators, such as the Green's function-based approach of Hamba, recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has been used to quantify RANS-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Schäfer and Owhadi (2023) to recover elliptic integral operators from a polylogarithmic number of matrix-vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix-vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first "peels" long-range effects with dense matrix-vector products to expose a local operator. We demonstrate the algorithm's performance for scalar transport in a laminar channel flow and momentum transport in a turbulent one. For these, we recover eddy diffusivity operators at 1% of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13% for the turbulent one. We observe that we can reconstruct these operators with an increase in accuracy by about a factor of 100 over randomized low-rank methods. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

physics.comp-ph↗

arXiv2023

A quantitative comparison of phase-averaged models for bubbly, cavitating flows

We compare the computational performance of two modeling approaches for the flow of dilute cavitation bubbles in a liquid. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected features, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and field equations for the associated bubble properties are evolved in an Eulerian reference frame. For polydisperse mixtures, the probability density function of the equilibrium bubble radii is discretized and bubble properties are solved for each representative bin. In both cases, the equations are closed by solving Rayleigh-Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. An acoustically excited dilute bubble screen is used as a case study for comparisons. We show that observables of ensemble- and volume-averaged simulations match closely and that their convergence is first order under grid refinement. Guidelines are established for phase-averaged simulations by comparing the computational costs of methods. The primary costs are shown to be associated with stochastic closure; polydisperse ensemble-averaging requires many samples of the underlying PDF and volume-averaging requires repeated, randomized simulations to accurately represent a homogeneous bubble population. The relative sensitivities of these costs to spatial resolution and bubble void fraction are presented.

physics.flu-dyn↗

arXiv2022

Application Experiences on a GPU-Accelerated Arm-based HPC Testbed

This paper assesses and reports the experience of ten teams working to port,validate, and benchmark several High Performance Computing applications on a novel GPU-accelerated Arm testbed system. The testbed consists of eight NVIDIA Arm HPC Developer Kit systems built by GIGABYTE, each one equipped with a server-class Arm CPU from Ampere Computing and A100 data center GPU from NVIDIA Corp. The systems are connected together using Infiniband high-bandwidth low-latency interconnect. The selected applications and mini-apps are written using several programming languages and use multiple accelerator-based programming models for GPUs such as CUDA, OpenACC, and OpenMP offloading. Working on application porting requires a robust and easy-to-access programming environment, including a variety of compilers and optimized scientific libraries. The goal of this work is to evaluate platform readiness and assess the effort required from developers to deploy well-established scientific workloads on current and future generation Arm-based GPU-accelerated HPC systems. The reported case studies demonstrate that the current level of maturity and diversity of software and tools is already adequate for large-scale production deployments.

cs.DC↗

arXiv2022

Competitive Physics Informed Networks

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy solutions, typically attaining about $0.1\%$ relative error. We present an adversarial approach that overcomes this limitation, which we call competitive PINNs (CPINNs). CPINNs train a discriminator that is rewarded for predicting mistakes the PINN makes. The discriminator and PINN participate in a zero-sum game with the exact PDE solution as an optimal strategy. This approach avoids squaring the large condition numbers of PDE discretizations, which is the likely reason for failures of previous attempts to decrease PINN errors even on benign problems. Numerical experiments on a Poisson problem show that CPINNs achieve errors four orders of magnitude smaller than the best-performing PINN. We observe relative errors on the order of single-precision accuracy, consistently decreasing with each epoch. To the authors' knowledge, this is the first time this level of accuracy and convergence behavior has been achieved. Additional experiments on the nonlinear Schrödinger, Burgers', and Allen-Cahn equation show that the benefits of CPINNs are not limited to linear problems.

cs.LG↗

arXiv2022

A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops

A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling of interfacial charge transport and fluid flow can trigger electrohydrodynamic instabilities that lead to shape deformations and complex dynamics. We present a spectral boundary integral method to simulate droplet electrohydrodynamics in a uniform electric field. All physical variables, such as drop shape and interfacial charge density, are represented using spherical harmonic expansions. In addition to its exponential accuracy, the spectral representation affords a nondissipative dealiasing method required for numerical stability. A comprehensive charge transport model, valid under a wide range of electric field strengths, accounts for charge relaxation, Ohmic conduction, and surface charge convection by the flow. A shape reparametrization technique enables the exploration of significant droplet deformation regimes. For low-viscosity drops, the convection by the flow drives steep interfacial charge gradients near the drop equator. This introduces numerical ringing artifacts we treat via a weighted spherical harmonic expansion, resulting in solution convergence. The method and simulations are validated against experimental data and analytical predictions in the axisymmetric Taylor and Quincke electrorotation regimes.

physics.flu-dyn↗