Search NASA⌕ Search

SEARCH · Search NASA

Results for “Differential model”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2023

Differentiable modelling to unify machine learning and physical models for geosciences

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. Here, in this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs.

58 GEOSCIENCES↗
DOE OSTI2025

Autonomous phase mapping of gold nanoparticles synthesis with differentiable models of spectral shape

Autonomous experimentation–or self-driving labs–offers a systematic approach to accelerate materials discovery by integrating automated synthesis, characterization, and data-driven decision-making. We present a closed-loop workflow for the on-demand synthesis and structural characterization of colloidal gold nanoparticles, enabling direct mapping from composition to nanoscale structure. Our framework leverages differentiable models of spectral shape to address two central tasks in self-driving labs: (a) phase mapping, or identifying compositional regions with distinct structural behavior; and (b) material retrosynthesis, or optimizing compositions for target structure. Using functional data analysis, we develop a data-driven model with generative pre-training, active learning, and high-throughput experiments to predict spectral responses across composition space. We demonstrate the approach on seed-mediated growth of gold nanoparticles, showcasing its ability to extract design rules, reveal secondary interactions, and efficiently navigate morphology space. Gradient-based optimization of the models enables inverse design, making this a unified platform.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Differentiable modeling and optimization of non-aqueous Li-based battery electrolyte solutions using geometric deep learning

Electrolytes play a critical role in designing next-generation battery systems, by allowing efficient ion transfer, preventing charge transfer, and stabilizing electrode-electrolyte interfaces. In this work, we develop a differentiable geometric deep learning (GDL) model for chemical mixtures, DiffMix, which is applied in guiding robotic experimentation and optimization towards fast charging battery electrolytes. In particular, we extend mixture thermodynamic and transport laws by creating GDL-learnable physical coefficients. We evaluate our model with mixture thermodynamics and ion transport properties, where we show improved prediction accuracy and model robustness of Diff-Mix than its purely data-driven variants. Furthermore, with a robotic experimentation setup, Clio, we improve ionic conductivity of electrolytes by over 18.8% within 10 experimental steps, via differentiable optimization built on DiffMix gradients. By combining GDL, mixture physics laws, and robotic experimentation, DiffMix expands the predictive modeling methods for chemical mixtures and enables efficient optimization in large chemical spaces.

25 - ENERGY STORAGE↗
DOE OSTI2023

A differentiable model of the evolution of dark matter halo concentration

ABSTRACT We introduce a new model of the evolution of the concentration of dark matter haloes, c(t). For individual haloes, our model approximates c(t) as a power law with a time-dependent index, such that at early times, concentration has a nearly constant value of c ≈ 3–4, and as cosmic time progresses, c(t) smoothly increases. Using large samples of halo merger trees taken from the Bolshoi–Planck and MultiDark Planck 2 cosmological simulations, we demonstrate that our three-parameter model can approximate the evolution of the concentration of individual haloes with a typical accuracy of 0.1 dex for $t\gtrsim 2\, {\rm Gyr}$ for all Bolshoi–Planck and MultiDark Planck 2 haloes of present-day peak mass $M_{0}\gtrsim 10^{11.5}\, {\rm M}_{\odot }$. We additionally present a new model of the evolution of the concentration of halo populations, which we show faithfully reproduces both average concentration growth and the diversity of smooth trajectories of c(t), including capturing correlations with halo mass and halo assembly history. Our publicly available source code, diffprof, can be used to generate Monte Carlo realizations of the concentration histories of cosmologically representative halo populations. diffprof is differentiable due to its implementation in the jax autodiff library, which facilitates the incorporation of our model into existing analytical halo model frameworks.

Stevanovich, Dash↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
DOE OSTI2023

Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling

Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is needed for convergence, and recent advances have made it possible to perform reconstruction with nonlinear models based on galaxy (or halo) positions. In addition to positions, future surveys will provide measurements of galaxies' peculiar velocities through the kinematic Sunyaev-Zel'dovich effect (kSZ), type Ia supernovae, the fundamental plane relation, and the Tully-Fisher relation. Here we develop the formalism for including halo velocities, in addition to halo positions, to enhance the reconstruction of the initial conditions. We show that using velocity information can significantly improve the reconstruction accuracy compared to using only the halo density field. Here we study this improvement as a function of shot noise, velocity measurement noise, and angle to the line of sight. We also show how halo velocity data can be used to improve the reconstruction of the final nonlinear matter overdensity and velocity fields. We have built our pipeline into the differentiable Particle-Mesh FlowPM package, paving the way to perform field-level cosmological inference with joint velocity and density reconstruction. This is especially useful given the increased ability to measure peculiar velocities in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Rare Lepton Decays and Differentiable Hadronization Models - From Signatures of New Physics to Data-driven Event Generation

This dissertation is partitioned into two parts: phenomenological studies focused on rare lepton decays as probes of heavy and light new physics, and the development of differentiable, data-driven hadronization models. Part I develops the phenomenology of new physics signatures stemming from rare charged lepton flavor violating decays probed by experiments at the intensity frontier. These include interactions mediated by both high-scale effective operators and light new physics, manifesting in multi-lepton final states ($\mu \to 5e$), elastic nuclear transitions ($\mu \to e$ conversion), baryon-number-violating muon capture, and time-dependent signals from ultralight dark matter ($\mu \to e \phi, \tau \to \ell \phi$). Part II develops two distinct strategies for advancing differentiable and data-driven hadronization models. One involves comprehensive reweighting frameworks for hadronization that enable efficient uncertainty estimation, facilitate parameter tuning, and interface naturally with differentiable programming paradigms. The other introduces machine-learning-based methods for extracting microscopic fragmentation dynamics directly from macroscopic observables through the deformation of existing models -- effectively providing solutions to the inverse problem of hadronization. Altogether, these studies advance the interpretability, flexibility, and precision of theoretical predictions for both high-intensity and high-energy experiments.

Menzo, Tony [Cincinnati U.] (ORCID:000000022013457↗
DOE OSTI2026

Interpretable Models for Workflow Differentiation in High-Performance Scientific Networks

Scientific workflows in high-performance networks spawn hundreds of interdependent flows that must be managed collectively—yet existing network classifiers treat each flow in isolation, leading to fragmented QoS decisions and missed interflow patterns. We present a novel traffic classification solution that operates at the workflow level, distinguishing entire filetransfer operations from streaming analytics by capturing how concurrent flows interact and burst together. We introduce a workflow identification window (WIW) that ingests raw packet headers from parallel flows into unified tensors, preserving the spatial-temporal patterns that differentiate scientific workflows. This approach achieves 98.7% accuracy using CNN, LSTM, and hybrid architectures, while maintaining 84% accuracy on production traffic collected a week later—demonstrating robustness to temporal drift. By integrating SHAP and GradCAM explainability, we reveal that early-packet timing patterns and cross-flow correlations drive classification decisions, providing operators with interpretable insights. Our system enables coherent workflow-level QoS enforcement and dynamic bandwidth allocation in scientific networks, eliminating manual per-flow configuration while maintaining classification latency at millisecond level.

Giannakou, Anna [LBL, Berkeley]↗
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 OSTI2025

Coarse-Grained Modeling Elucidates Differential Metabolism of Saccharomyces cerevisiae under Varied Nutrient Limitations

Microorganisms such as Saccharomyces cerevisiae have a native ability to adapt their metabolism to varying nutrient conditions. Understanding their responses to nutrient limitations is critical for decoding cellular physiology and designing strategies for metabolic engineering. While the influence of carbon availability on yeast metabolism has been extensively studied, the role of nitrogen availability remains relatively underexplored. In this study, we utilized a coarse-grained kinetic model to systematically analyze and compare the effects of carbon and nitrogen limitations on yeast metabolism. Our model successfully revealed the differential metabolic characteristics of S. cerevisiae under carbon- and nitrogen-limited chemostat conditions. It also highlighted the significance of protein activity regulation at varying carbon-to-nitrogen ratios, and elucidated distinct strategies employed to maintain ATP homeostasis. Furthermore, this study provides a computational tool for investigating yeast physiology under nutrient limitations and offers quantitative and mechanistic insights into yeast metabolism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Improving River Routing Using a Differentiable Muskingum‐Cunge Model and Physics‐Informed Machine Learning

Recently, rainfall-runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics-NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC-Juniata-hydroDL2) that mimics the classical Muskingum-Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real-world data, the trained differentiable routing model produced more accurate long-term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national-scale hydrologic flood simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

JAX-CanVeg: A Differentiable Land Surface Model

Land surface models consider the exchange of water, energy, and carbon along the soil-canopy-atmosphere continuum, which is challenging to model due to their complex interdependency and associated challenges in representing and parameterizing them. Differentiable modeling provides a new opportunity to capture these complex interactions by seamlessly hybridizing process-based models with deep neural networks (DNNs), benefiting both worlds, that is, the physical interpretation of process-based models and the learning power of DNNs. Here, we developed a differentiable land model, JAX-CanVeg. The new model builds on the legacy CanVeg by incorporating advanced functionalities through JAX in the graphic processing unit support, automatic differentiation, and integration with DNNs. We demonstrated JAX-CanVeg's hybrid modeling capability by applying the model at four flux tower sites with varying aridity. To this end, we developed a hybrid version of the Ball-Berry equation that emulates the water stress impact on stomatal closure to explore the capability of the hybrid model in (a) improving the simulations of latent heat fluxes (LE) and net ecosystem exchange (NEE), (b) improving the optimization trade-off when learning observations of both LE and NEE, and (c) benefiting a multi-layer canopy model setup. Our results show that the proposed hybrid model improved the simulations of LE and NEE at all sites, with an improved optimization trade-off over the process-based model. Additionally, the multi-layer canopy set benefited hybrid modeling at some sites. Anchored in differentiable modeling, our study provides a new avenue for modeling land-atmosphere interactions by leveraging the benefits of both data-driven learning and process-based modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks

Abstract The constitutive relations of the Richardson‐Richards equation encode the macroscopic properties of soil water retention and conductivity. These soil hydraulic functions are commonly represented by models with a handful of parameters. The limited degrees of freedom of such soil hydraulic models constrain our ability to extract soil hydraulic properties from soil moisture data via inverse modeling. We present a new free‐form approach to learning the constitutive relations using physically constrained neural networks. We implemented the inverse modeling framework in a differentiable modeling framework, JAX, to ensure scalability and extensibility. For efficient gradient computations, we implemented implicit differentiation through a nonlinear solver for the Richardson‐Richards equation. We tested the framework against synthetic noisy data and demonstrated its robustness against varying magnitudes of noise and degrees of freedom of the neural networks. We applied the framework to soil moisture data from an upward infiltration experiment and demonstrated that the neural network‐based approach was better fitted to the experimental data than a parametric model and that the framework can learn the constitutive relations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

A buoyancy–shear–drag–scalar-based turbulence model for power-law acceleration-driven Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A previously developed phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing based on a general buoyancy–shear–drag model [O. Schilling, “A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing,” Physica D 402, 132238 (2020)] is extended to include active or passive scalar mixing and power-law acceleration-driven Rayleigh–Taylor mixing. The buoyancy–shear–drag equations are coupled to a scalar variance equation that is used to define the molecular mixing parameter θ m , and when the scalar is active, modifies the Rayleigh–Taylor and Kelvin–Helmholtz mixing layer growth parameters to depend on the asymptotic value of this parameter, θ mol . Here, the scalar variance equation is closed by algebraically or differentially modeling the scalar variance dissipation rate. Nonlinear analytical solutions of the model are obtained in the total and separate bubble and spike mixing layer width formulations with the algebraic scalar variance dissipation rate for each instability, which are then used to calibrate the mechanical and scalar equation coefficients to predict specific values of physical observables and molecular mixing parameters. Surrogate mechanical and scalar turbulent fields can be constructed by multiplying a presumed self-similar spatial profile by appropriate functions of the width and its time derivative, and of the scalar obtained by solving the ordinary differential model equations. The explicit modeling and solution of turbulent transport equations are not required. The bubble and spike mixing layer width and scalar variance equations are then solved numerically for constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing, confirming that the prescribed level of molecular mixing is correctly predicted and illustrating the spatiotemporal evolution of the scalar fields.

Buoyancy–drag↗