Search NASASearch

SEARCH · Search NASA

Results for “Differentiable programming”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Fuel-Cladding Eutectic Study of Legacy Fast Flux Test Facility (FFTF) MFF HT9/U-10Zr Metallic Fuel

This report presents the first systematic investigation of fuel-cladding eutectic interaction (FCEI) in irradiated HT9/U-10Zr metallic fuel from the Fast Flux Test Facility (FFTF) Materials Fuels Form (MFF) program, using differential scanning calorimetry (DSC) coupled with scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Two irradiated fuel cross-sections, MNT07H (9.5 at% burnup, x/L = 0.78) and MNT08H (7.0 at% burnup, x/L = 0.93), were subjected to three successive isothermal annealing rounds (R1–R3) at 820°C for 20 minutes each, yielding a cumulative transient duration of one hour. This study directly addresses a recognized gap in the existing FCEI database, which previously lacked irradiated HT9/U-10Zr data at burnup levels above 8 at%. Two principal findings emerge from the study. First, for both samples, FCEI remained spatially confined within the pre-existing fuel-cladding chemical interaction (FCCI) zone boundaries after R3, with no measurable eutectic penetration into unaffected cladding beyond the original FCCI layer. This self-limiting behavior is consistent with historical Fuel Behavior Test Apparatus (FBTA) results and is attributed to the near-eutectic phase composition of the FCCI zone, which rapidly absorb the available eutectic-forming constituents and then stall penetration once the FCCI zone is consumed. A comparison with unirradiated surrogate data further supports this mechanism: whereas a U–34 at.% Fe sample would be expected to show ~176 µm of iron penetration under comparable conditions, the irradiated samples exhibited only ~20 µm, a discrepancy attributed to irradiation-induced interfacial porosity and pre-existing FCCI composition gradients. Second, for MNT08H, FCEI was observed exclusively on the half of the cladding circumference where pre-existing steady-state FCCI was present, with no detectable FCEI on the opposite half. Three hypotheses are proposed to explain this asymmetry: the inhibiting role of a zirconium-rich rind at the fuel-cladding interface; the chemical sequestration of iron by redistributed zirconium within the fuel matrix; and the persistence of fuel-cladding gaps on the FCEI-free half that preclude direct contact. All three hypotheses require further experimental investigation. The results extend the empirical FCEI database into higher-burnup territory and demonstrate the viability of DSC-based testing as a substitute for the no-longer-available FBTA apparatus. Future work will include additional cross-section testing, compilation of the full FCEI dataset, model evaluation, and DSC testing of ternary fuel compositions to broaden the experimental basis for safety assessment of sodium-cooled fast reactor systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

A multi-language auto differentiation package (mAD) v1.0

This is a multi-language auto differentiation package. It includes multiple language versions of the package. It can be included/used as a module/class in users' application program to enable differentiability of the program. It is simple, transparent, extensible, efficient compared with the other AD package such as Enzyme or Pytorch.

Qiang, Ji [Lawrence Berkeley National Laboratory (

A taxonomy of automatic differentiation pitfalls

Automatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time-averages, discretizations, fixed-point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.

Autodiff

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Cross Section Evaluation for Exclusive Channels of K+Λ and K+Σ0 Electroproduction off Protons Using CLAS Detector Data

In this work, a method for evaluating the cross sections of electroproduction of K+Λ0 and K+Σ0 off protons in the region of invariant masses of final hadrons MK + MY <W < 2.65 GeV (MK and MY being the masses of the kaon and hyperon, respectively) and squares of four-momentum transfers of virtual photons, i.e., photon virtualities 0 < Q2 < 5 GeV2, is developed based on experimental data of these exclusive channels’ cross sections measured by the CLAS detector in Hall B at Jefferson Lab. A set of algorithms has been implemented to evaluate the differential cross sections of these channels, along with their statistical and systematic uncertainties. A program was developed for the evaluation of differential cross sections and structure functions using C++ and Python libraries. An interactive website was created for working with the program, enabling the analysis of one-dimensional and two-dimensional dependences of structure functions and differential cross sections. The evaluation of differential cross sections for the K+Λ and K+Σ0 electroproduction channels is necessary for extracting the structure function σLT from the data on the polarization asymmetry of electroproduction reactions of these final states with longitudinally polarized electrons. The obtained results are also important for the development of realistic Monte Carlo event generators in planning future experiments and for evaluating the efficiency of detecting final particles when extracting reaction cross sections from experimental data.

Golda, A. V.

Unified differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or produce insights about accelerator state. One notable example of additional information are gradients of physical observables with respect to design parameters produced by differentiable simulations. The IOTA/FAST facility has recently begun a program to implement and experimentally validate a unified start-to-end differentiable digital twin to serve as a virtual accelerator test stand, allowing for rapid prototyping of new software and experiments with minimal beam time costs. In this contribution we will discuss our plans and progress. Specifically, we will cover the selection and benchmarking of both physics and ML codes, the development of generic interfaces between device models and surrogate or physics-based sections, and the export of the parameters through either a deterministic event loop or a fully asynchronous EPICS soft input/output controller. We will also discuss challenges in model calibration and uncertainty quantification, as well as future plans to support larger proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]

Scrutinizing Variables for Checkpoint Using Automatic Differentiation

Checkpoint/Restart (C/R) saves the running state of the programs periodically, which consumes considerable time and system resources. We observe that not every piece of data is involved in the computation in typical HPC applications; such unused data should be excluded from checkpointing for better storage and compute efficiency. We propose a systematic approach that leverages automatic differentiation (AD) to scrutinize every element within variables (e.g., arrays) necessary for checkpointing. This allows us to identify critical and uncritical elements and eliminate uncritical elements from checkpointing. Specifically, we inspect every single element within a variable necessary for checkpointing with an AD tool to determine whether the element has an impact on the application output or not. We validate our approach with all benchmarks from the NPB suite. We visualize the distribution of critical and uncritical elements within a variable with respect to its binary impact (yes or no) on the application output.

Huang, Xin [Kobe University]

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions

Metric Learning to Accelerate Convergence of Operator Splitting Methods

Recent developments in machine learning have led to promising advances in accelerating the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial intelligence and optimal control has led to a variety of proposed strategies for learning to produce fast solutions to optimization problems. For example, recent works have shown that it is possible to accelerate the convergence of optimization algorithms by learning to select their parameters, such as gradient descent stepsizes. This work proposes a new approach, in which the underlying metric spaces of proximal operator splitting algorithms are learned to maximize convergence rate. While prior works in optimization theory have derived optimal metrics in simple cases, no such result exists for many practical problem forms including general Quadratic Programming (QP). This paper shows how differentiable optimization can enable the end-to-end learning of proximal metrics, enhancing the convergence of proximal algorithms for QP problems beyond what is possible based on known theory. Additionally, the results illustrate a strong connection between the learned proximal metrics and active constraints at the optima, leading to an interpretation in which the predicted proximal metrics can be viewed as a form of active set prediction.

King, Ethan [BATTELLE (PACIFIC NW LAB)]

JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking

Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.

43 PARTICLE ACCELERATORS

Status of 1eNp0π Charged-Current Electron Neutrino Cross Section on Argon in the NuMI Beam at ICARUS

The Short-Baseline Neutrino (SBN) Program is designed to probe short-baseline neutrino anomalies, including the LSND electron neutrino excess and the MiniBooNE low-energy excess. Essential to interpreting these anomalies and to the success of future experiments like DUNE, is the precise measurement of neutrino-argon interaction cross sections. The program utilizes two liquid argon time projection chamber (LArTPC) detectors: the Short-Baseline Near Detector (SBND) located 110 meters downstream from the Booster Neutrino Beam (BNB) target, and the ICARUS detector positioned 600 meters downstream. Additionally, the ICARUS detector lies off-axis to the NuMI beamline, providing a unique, high-statistics flux of electron neutrinos and sensitivity to energies that overlap with the DUNE spectrum. To analyze the data from these detectors, we have begun employing a machine-learning-based reconstruction algorithm referred to as “Scalable Particle Imaging with Neural Embeddings” (SPINE). SPINE has shown improvement in the ability to reconstruct the properties of final state particles in the detector, like the particle ID and momentum, with the potential to enhance the quality of measurements achievable within the SBN Program e.g., the resolution on kinematics used in differential cross section extraction. This poster presents progress toward measuring the electron neutrino argon interaction cross section in the 1eNp0π topology using the NuMI beam, highlighting the impact of SPINE through the ability to select signal events across a wide kinematic range without sacrificing background rejection power.

Carber, Dan [Colorado State U.] (ORCID:00090006451

End-to-end differentiable digital twin for the IOTA/FAST facility

As the design complexity of modern accelerators grows, there is more interest in using controllable-fidelity simulations that have fast execution time or can yield additional insights about accelerator state. One notable example of additional information are gradients of physical observables with respect to design parameters produced by differentiable simulations. The IOTA/FAST facility has recently begun a program to implement and experimentally validate an end-to-end digital twin to serve as a virtual accelerator test stand, allowing for rapid prototyping of new software and experiments with minimal beam time costs. In this contribution we will discuss our plans and progress. Specifically, we will cover the selection and benchmarking of both physics and ML codes for linac and ring simulation, the development of generic interfaces between surrogate and physics-based sections, and presenting the control interface as either a deterministic event loop or a fully asynchronous EPICS soft input/output controller. We will also discuss challenges in model calibration and uncertainty quantification, as well as future plans to implement larger proton accelerators like PIPII and Booster.

Kuklev, N. [Fermilab]

FSEN Reaction Rate Calculations in MCNP [Slides]

FSEN provides an opportunity to quickly calculate sensitivities to orthogonal measurements during integral experiments. Toy problem has been deployed to expand on verification of FSEN for reaction rate ratios. While there is decent agreement, further investigation must be done on multiplication’s impact on sensitivity vector.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

The PARADIGM Project: Case Study in Balancing Experiment Uncertainty with Design simplicity

Accurate nuclear data are required for simulations of many applications including nuclear criticality safety. Actinide nuclear data at intermediate energies (from 1 to 100s of keV) are imprecise and inaccurate, because of scarce differential data, and an insufficient theory approach to capture the structures expected in the data to yield evaluated nuclear data, and lack of integral data for proper validation. This is a known deficiency but has proved challenging to address. More specifically, only 5% of integral experiments in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmark suite address intermediate energies (Fig. 1). Associated calculated effective multiplication factor, k eff , values for these experiments are far outside the experimental uncertainties and are 25× further from experiment than for fast energies. These differences could either stem from systematic biases in nuclear data, experiments or both. The goal of the PARADIGM (PARallel Approach of Differential and InteGral Measurements) project is to significantly reduce (by more than tens of percent) the uncertainties of intermediate energy actinide nuclear data. The PARADIGM project designed and intends to execute LANSCE (Los Alamos Neutron Science CEnter) and NCERC (National Criticality Experiments Research Center) intermediate experiments in parallel. They will specifically address a high priority nuclear data need—reducing bias and uncertainty in intermediate plutonium nuclear data. The two experiment will achieve that by informing each other and nuclear theory. By doing all these steps in parallel, the timeline to deliver improved nuclear data to users will significantly be reduced. This work will focus on the integral experiment final design and the balance of design and modeling simplicity while minimizing experiment uncertainty.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

HIGH BURNUP FUEL-COOLANT INTERACTION ANALYSIS SUPPORTING FUEL SAFETY TESTING AT IDAHO NATIONAL LABORATORY

In the near future, experiments on HBu fuel under loss-of-coolant accident (LOCA) and reactivity-initiated accident (RIA) conditions will be performed within the Transient Reactor Test Facility (TREAT) at Idaho National Laboratory (INL). These experiments will be performed using the Transient Water Irradiation System for TREAT (TWIST) experiment vehicle. To support these experiments, analysis of fuel-coolant interaction (FCI) energetics is underway. This paper discusses FCIs in the context of light water reactor (LWR) safety, differentiating between the severe accident focus of commercial reactors and experimental RIA test programs where FCIs have occurred. However, it is highlighted that as the nuclear industry aims for increased burnup limits, the FCI events observed in RIA test programs may become relevant to commercial LWR safety analysis. The paper then presents developments to the UW-FCI computer program to enable simulation of FCIs initiated by solid fuel particles dispersing into the coolant during RIAs.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS