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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the polynomial order used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Verification of the DIF3D Software to Support Fast Reactor Analysis

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Verification of the DIF3D Software to Support Fast Reactor Analysis (Rev. 3)

Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system. The driver for this effort requires the 3D Cartesian, triangular-Z, and hexagonal-Z core geometry options of DIF3D be verified. Previous work identified the DIF3D features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying DIF3D’s ability to correctly translate the user’s model in to DIF3D’s preferred format, verifying that options planned for use have the desired effect, and verifying the correctness of the eigenvalue, fixed-source, forward, and adjoint solvers in DIF3D-FD and DIF3D-VARIANT. This manuscript provides the verification tasks and their results with respect to the features needed for current design activities. Since analytic solutions of the neutron diffusion and transport equations are either limited in scope or not possible, multiple tiers of problems unique to each solver and geometry type were implemented. Each of these tiers tests features independent and complementary arguments for why the separate testing of functionalities is acceptable. Finally, this separate testing was also supplemented with a high-level integral check of each the diffusion and transport capabilities and applicable geometries. To accommodate cases which an analytic solution is not feasible, MCNP6.2 was relied upon to provide a higher-order reference solution. This therefore required that the capabilities within MCNP6.2 which were relied upon for this work are also verified in this work. No MCNP discrepancies were noted in this effort. Note that the MCNP6.2 verification included in this work does not stand as a full verification of MCNP6.2, but merely verifies the features used in verifying DIF3D. The verification effort identified no issues that are debilitating or otherwise impactful to design usage of DIF3D, and thus DIF3D version 11.0, release 3012 is considered verified. As some additional changes have been made to the ARC software since this point all versions between release 3012 and 3266 can be considered verified as version 3253 was used for all updates in this revision. The types of issues that were identified were predominantly in the areas of: unclear documentation, software bugs which were inconsequential to final results, editing options which were ignored in favor of printing more information than requested, bugs in the outputs of intermediate results, or secondary output binary file information which was not present. While not a bug, this verification report also identified that the algorithm used to evaluate the peak fast flux in a nodal transport solution can be quite unreliable due to the methodology used and the location of the peak within the mesh. The authors of the report therefore recommend the usage of the EvaluateFlux software (distributed with ARC) as a more robust alternative noting that DIF3D will properly notify the user when the peaking values it is providing are potentially incorrect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗
DOE OSTI2020

Blood flow imaging by optimal matching of computational fluid dynamics to 4D-flow data

Three-dimensional, time-resolved blood flow measurement (4D-flow) is a powerful research and clinical tool, but improved resolution and scan times are needed. Therefore, this study aims to (1) present a postprocessing framework for optimization-driven simulation-based flow imaging, called 4D-flow High-resolution Imaging with a priori Knowledge Incorporating the Navier-Stokes equations and the discontinuous Galerkin method (4D-flow HIKING), (2) investigate the framework in synthetic tests, (3) perform phantom validation using laser particle imaging velocimetry, and (4) demonstrate the use of the framework in vivo. An optimizing computational fluid dynamics solver including adjoint-based optimization was developed to fit computational fluid dynamics solutions to 4D-flow data. Synthetic tests were performed in 2D, and phantom validation was performed with pulsatile flow. Reference velocity data were acquired using particle imaging velocimetry, and 4D-flow data were acquired at 1.5 T. In vivo testing was performed on intracranial arteries in a healthy volunteer at 7 T, with 2D flow as the reference. Results Synthetic tests showed low error (0.4%-0.7%). Phantom validation showed improved agreement with laser particle imaging velocimetry compared with input 4D-flow in the horizontal (mean -0.05 vs -1.11 cm/s, P < .001; SD 1.86 vs 4.26 cm/s, P < .001) and vertical directions (mean 0.05 vs -0.04 cm/s, P = .29; SD 1.36 vs 3.95 cm/s, P < .001). In vivo data show a reduction in flow rate error from 14% to 3.5%. Phantom and in vivo results from 4D-flow HIKING show promise for future applications with higher resolution, shorter scan times, and accurate quantification of physiological parameters.

4D-flow MRI↗
DOE OSTI2021

Juqbox.jl

The Juqbox.jl package implements functionality for solving the quantum optimal control problem for realizing logical gates in closed quantum systems. The dynamics of the quantum system is modeled by Schroedinger's equation, which takes to form of a linear system of ordinary differential equations (ODE). Juqbox.jl solves this ODE by numerical time stepping and applies a gradient-based optimization technique to determine control pulses for driving an initial state to a final state, according to the desired logical gate transformation. To evaluate the gradient, Juqbox.jl applies the ``first discretize, then optimize'' approach based on a discrete adjoint time stepping technique. The actual optimization is performed by the open source Ipopt libaray. Juqbox.jl is written in the Julia programming language which, among many other features, provides a convenient interface to the Ipopt library.

PETERSSON, NILSA.↗
DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗
DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2022

Causal diamonds, cluster polytopes and scattering amplitudes

The “amplituhedron” for tree-level scattering amplitudes in the bi-adjoint φ 3 theory is given by the ABHY associahedron in kinematic space, which has been generalized to give a realization for all finite-type cluster algebra polytopes, labelled by Dynkin diagrams. In this letter we identify a simple physical origin for these polytopes, associated with an interesting (1 + 1)-dimensional causal structure in kinematic space, along with solutions to the wave equation in this kinematic “spacetime” with a natural positivity property. The notion of time evolution in this kinematic spacetime can be abstracted away to a certain “walk”, associated with any acyclic quiver, remarkably yielding a finite cluster polytope for the case of Dynkin quivers. The A n–3 , B n–1 /C n–1 and D n polytopes are the amplituhedra for n-point tree amplitudes, one-loop tadpole diagrams, and full integrand of one-loop amplitudes. We also introduce a polytope D¯ n , which chops the D n polytope in half along a symmetry plane, capturing one-loop amplitudes in a more efficient way.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

An autoencoder compression approach for accelerating large-scale inverse problems

Abstract Partial differential equation (PDE)-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes required to accurately compute the PDE solution introduce an enormous number of parameters and require large-scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time-dependent PDEs, the adjoint method often employed to compute gradients and higher order derivatives efficiently requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high-dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior showing how the DIAS method can be affordably extended to large-scale problems without the need for checkpointing and large memory.

Mathematics↗
DOE OSTI2022

Adjoint sensitivity analysis and data assimilation for verification of dry storage cask contents

Dry cask storage is a method for interim storage of spent fuel assemblies which contain fissile isotopes of uranium and plutonium. These can present a proliferation concern and consequently there is a need for non-destructive testing methods to verify a dry cask's contents for proliferation protection. We present an application of adjoint sensitivity analysis and data assimilation to a multigroup diffusion model of dry cask storage. Adjoint sensitivity analysis allows the efficient calculation of sensitivities for use in data assimilation to calibrate imprecisely known parameter values and data consistency tests to detect diversion scenarios. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Reduced-order modeling of neutron transport separated in energy by Minimax Proper Generalized Decomposition

In this article, we demonstrate a Petrov-Galerkin Proper Generalized Decomposition (PGD) known as Minimax PGD for modeling neutron transport separated in energy. To compare the Minimax with the classical Galerkin PGD, we assess both on a model problem of UO{sub 2} or Mixed Oxide (MOX) fuel pins in an infinite lattice with 3 industry-standard energy meshes. We find the Minimax PGD achieves a superior decomposition to Galerkin PGD, both with and without update of the energy modes. This suggests Minimax PGD may be more computationally efficient, provided this reduction in modes (to achieve a given accuracy) outweighs the cost of solving the necessary adjoint problems. In either case, we note that PGD offers an a priori Reduced-Order Model (ROM) which may be dramatically cheaper to solve than the full-order model, especially in problems with fine to ultrafine energy meshes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the Definition of the Prompt Neutron Lifetime

There are myriad definitions for the mean neutron lifetime, neutron generation time, and other related quantities to characterize a neutron and its progeny’s propagation through an assembly. In this document, we consider lifetime definitions that are associated with eigenvalue forms of the neutron transport equation. Specifically, we focus on the two most widely used eigenvalues: the $\kappa$ eigenvalue and the $\alpha$ eigenvalue. These eigenvalues are used more often than other eigenvalues due to the physical phenomenon they capture. The $\kappa$ eigenvalue allows for the ability to determine if the system can sustain a chain reaction, while the $\alpha$ eigenvalue captures the asymptotic time dependent behavior of the system. An advantage of using these eigenvalues resides in the biorthogonality of the solutions with their adjoint counterpart. This feature allows us to simplify the expressions and to obtain appropriately weighted definitions that highlight important physics and regions of an assembly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗