Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Automatic Differentiation”

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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dose-efficient automatic differentiation for ptychographic reconstruction

Ptychography, as a powerful lensless imaging method, has become a popular member of the coherent diffractive imaging family over decades of development. The ability to utilize low-dose X-rays and/or fast scans offers a big advantage in a ptychographic measurement (for example, when measuring radiation-sensitive samples), but results in low-photon statistics, making the subsequent phase retrieval challenging. Here, we demonstrate a dose-efficient automatic differentiation framework for ptychographic reconstruction (DAP) at low-photon statistics and low overlap ratio. As no reciprocal space constraint is required in this DAP framework, the framework, based on various forward models, shows superior performance under these conditions. It effectively suppresses potential artifacts in the reconstructed images, especially for the inherent periodic artifact in a raster scan. We validate the effectiveness and robustness of this method using both simulated and measured datasets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

POSTER: Automatic Differentiation of Parallel Loops with Formal Methods

The accompanying poster to this short paper presents a combination of reverse mode AD and formal methods to enable efficient differentiation of (or backpropagation through) shared-memory parallel code. Compared to the state of the art, our approach can more often avoid the need for atomic updates or private data copies during the parallel derivative computation, even in the presence of unstructured or data-dependent data access patterns. This is achieved by gathering information about the memory access patterns from the input program, which is assumed to be correctly parallelized. This information is then used to build a model of assertions in a theorem prover, which can be used to check the safety of shared memory accesses during the parallel derivative computation

Automatic Differentiation↗
DOE OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗
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 OSTI2023

Reconstruction of simulated electrostatic potentials by automatic differentiation-based phase retrieval in electron microscopy imaging

Measuring interfacial electrostatic potentials is vital to understanding many fundamental materials properties. A variety of TEM methods exist for measuring electric potentials from the phase shift produced on an electron wave as it passes through a sample. However, most are either experimentally challenging or poorly suited to resolving nanoscale features. Here, we demonstrate the viability of a simple, automatic differentiation-based exit wave reconstruction from a focal series of images to accurately measure nanoscale electric potentials. Here, the analysis suggests that under optimal measurement conditions, electric potentials can be resolved to less than 0.06 V in magnitude and less than 1 nm in spatial extent.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Degrees of rate control and AutoDiff-driven direct sensitivity analysis in heterogeneous catalysis

Despite the wide application and benefits of the degree of rate control (DRC) analysis, several details remain argued, particularly about the conservation of DRCs at transient (TR) and steady-state (SS) conditions, especially for complex reaction networks. This work argues that previous proofs about the conservation properties of DRCs have been incomplete, and we provide new mathematical proofs at TR and SS conditions. In addition, we use both analytical (automatic differentiation) and numerical (finite difference) approaches to compute DRCs for the case study of ethane hydrogenolysis (EH) over Pt(111). This work confirms that at both TR and SS conditions, the sum of all DRCs, i.e., sum of the degrees of kinetic (DKRC) and thermodynamic rate control (DTRC), is conserved at zero. At SS conditions, the sum of DKRC is conserved at 1 while the sum of DTRC is conserved at −1. In corroboration of previous works, we show that the DTRC for any adsorbate at SS is equal to the product of the species coverage and a constant. In contrast, at TR conditions, the individual sums of both DTRC and DKRC are not conserved and can be any real number, with potential implications for the novel field of dynamic catalysis. Finally, we show that the conventional finite difference (FD) approach, only useful at SS, is prone to inaccuracy and very sensitive to the value of the differential change applied. The optimal differential value also varies significantly with system and rate definition. Consequently, we describe and illustrate in this work the application of the automatic differentiation (AD) approach for the more accurate determination of DRCs at both TR and SS conditions.

Automatic differentiation↗
DOE OSTI2025

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↗
DOE OSTI2022

Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond

We introduce an extension to the PySCF package, which makes it automatically differentiable. The implementation strategy is discussed, and example applications are presented to demonstrate the automatic differentiation framework for quantum chemistry methodology development. These include orbital optimization, properties, excited-state energies, and derivative couplings, at the mean-field level and beyond, in both molecules and solids. We also discuss some current limitations and directions for future work.

Chemistry↗
DOE OSTI2021

End-to-End Differentiable Modeling and Management of the Environment

Focal Area: (2) Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization. We emphasize the importance of leveraging optimization techniques from AI/machine learning (ML) to solve challenging problems in Earth system modeling. Science Challenge: Automatic differentiation has had a transformative effect on ML by allowing the calculation of gradients of arbitrary functions in an incredibly large class of models. We can potentially realize similar improvements in parameter estimation and control for Earth system models (ESMs) by reimplementing them in computational frameworks from ML. Practitioners working with large (>10 7 parameters) models in ML and AI can obtain good predictive performance in a range of spatiotemporal tasks by making use of optimization via stochastic gradient descent and incorporating prior knowledge at multiple levels. We propose writing ESMs in open-source computational frameworks such as Torch, Tensorflow, and JAX to greatly expand the scope of environmental forecasting and management challenges, which can be addressed by leveraging automatic differentiation and gradient descent-like algorithms. We do not call for a wholesale replacement of physical models with data-driven surrogates, but rather advocate for interleaving physical and empirical equations in a manner that is most faithful to the extent of our scientific knowledge and observational data. Central to this topic is the merging of differentiable physical simulations with differentiable optimization layers, which are now both beginning to come to the forefront.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗
DOE OSTI2026

Ground and excited state gradients with end-to-end differentiable semiempirical quantum chemistry

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗