An improved static diffusion model of the thermosphere
Static diffusion model of thermosphere with allowance for temperature and chemical composition and not limited by constant 120 km boundary conditions
Chambers, J. L.↗
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Results for “Diffusion model”
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Accelerating Markov Chain Monte Carlo sampling with diffusion models
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Discrete generative diffusion models without stochastic differential equations: A tensor network approach
Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025
Causer, Luke (ORCID:0000000194243473)↗
Absorption of ethanol, acetone, benzene and 1,2-dichloroethane through human skin in vitro: a test of diffusion model predictions
The overall goal of this research was to further develop and improve an existing skin diffusion model by experimentally confirming the predicted absorption rates of topically-applied volatile organic compounds (VOCs) based on their physicochemical properties, the skin surface temperature, and the wind velocity. In vitro human skin permeation of two hydrophilic solvents (acetone and ethanol) and two lipophilic solvents (benzene and 1,2-dichloroethane) was studied in Franz cells placed in a fume hood. Four doses of each {sup 14}C-radiolabed compound were tested — 5, 10, 20, and 40 μL cm{sup −2}, corresponding to specific doses ranging in mass from 5.0 to 63 mg cm{sup −2}. The maximum percentage of radiolabel absorbed into the receptor solutions for all test conditions was 0.3%. Although the absolute absorption of each solvent increased with dose, percentage absorption decreased. This decrease was consistent with the concept of a stratum corneum deposition region, which traps small amounts of solvent in the upper skin layers, decreasing the evaporation rate. The diffusion model satisfactorily described the cumulative absorption of ethanol; however, values for the other VOCs were underpredicted in a manner related to their ability to disrupt or solubilize skin lipids. In order to more closely describe the permeation data, significant increases in the stratum corneum/water partition coefficients, K{sub sc}, and modest changes to the diffusion coefficients, D{sub sc}, were required. The analysis provided strong evidence for both skin swelling and barrier disruption by VOCs, even by the minute amounts absorbed under these in vitro test conditions. - Highlights: • Human skin absorption of small doses of VOCs was measured in vitro in a fume hood. • The VOCs tested were ethanol, acetone, benzene and 1,2-dichloroethane. • Fraction of dose absorbed for all compounds at all doses tested was less than 0.3%. • The more aggressive VOCs absorbed at higher levels than diffusion model predictions. • We conclude that even small exposures to VOCs temporarily alter skin permeability.
60 APPLIED LIFE SCIENCES↗
Derivation of effective fission gas diffusivities in UO2 from lower length scale simulations and implementation of fission gas diffusion models in BISON
This report summarizes the development of new fission gas diffusion models from lower length scale simulations and assessment of these models in terms of annealing experiments and fission gas release simulations using the BISON fuel performance code. Based on the mechanisms established from density functional theory (DFT) and empirical potential calculations, continuum models for diffusion of xenon (Xe) in UO 2 were derived for both intrinsic conditions and under irradiation. The importance of the large X eU 3 O cluster (a Xe atom in a uranium + oxygen vacancy trap site with two bound uranium vacancies) is emphasized, which is a consequence of its high mobility and stability. These models were implemented in the MARMOT phase field code, which is used to calculate effective Xe diffusivities for various irradiation conditions. The effective diffusivities were used in BISON to calculate fission gas release for a number of test cases. The results are assessed against experimental data and future directions for research are outlined based on the conclusions.
36 MATERIALS SCIENCE↗
Denoising diffusion models with geometry adaptation for high fidelity calorimeter simulation
Simulation is crucial for all aspects of collider data analysis, but the available computing budget in the High Luminosity LHC era will be severely constrained. Generative machine learning models may act as surrogates to replace physics-based full simulation of particle detectors, and diffusion models have recently emerged as the state of the art for other generative tasks. Here, we introduce CaloDiffusion, a denoising diffusion model trained on the public CaloChallenge datasets to generate calorimeter showers. Our algorithm employs 3D cylindrical convolutions, which take advantage of symmetries of the underlying data representation. To handle irregular detector geometries, we augment the diffusion model with a new geometry latent mapping (GLaM) layer to learn forward and reverse transformations to a regular geometry that is suitable for cylindrical convolutions. The showers generated by our approach are nearly indistinguishable from the full simulation, as measured by several different metrics.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Generative design of de novo proteins based on secondary-structure constraints using an attention-based diffusion model
We report two generative deep-learning models that predict amino acid sequences and 3D protein structures on the basis of secondary-structure design objectives via either the overall content or the per-residue structure. Both models are robust regarding imperfect inputs and offer de novo design capacity because they can discover new protein sequences not yet discovered from natural mechanisms or systems. The residue-level secondary-structure design model generally yields higher accuracy and more diverse sequences. These findings suggest unexplored opportunities for protein designs and functional outcomes within the vast amino acid sequences beyond known proteins. Our models, based on an attention-based diffusion model and trained on a dataset extracted from experimentally known 3D protein structures, offer numerous downstream applications in the conditional generative design of various biological or engineering systems. Future work could include additional conditioning and an exploration of other functional properties of the generated proteins for various properties beyond structural objectives.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization
Here in this paper, we first propose a nonlocal convection–diffusion model, in which the convection term is constructed in a special upwind manner so that mass conservation and maximum principle are maintained in any space dimension. The well-posedness of the proposed nonlocal model and its convergence to the classical local convection–diffusion model are established. A quadrature-based finite difference discretization is then developed to numerically solve the nonlocal problem and it is shown to be consistent and unconditionally stable. We further demonstrate that the numerical scheme is asymptotically compatible, that is, the approximate solutions converge to the exact solution of the corresponding local problem when δ → 0 and h → 0. Numerical experiments are also performed to complement the theoretical analysis.
42 ENGINEERING↗
Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a computational framework, regularization by denoising using diffusion models for partial differential equations (RED-DiffEq), by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to benchmark methods. Additionally, it exhibits strong generalization and domain decomposition capacity, enabling the inversion of more complex velocity models with larger domains than those used in training the diffusion model. Our framework can also be directly applied to diverse PDE-governed inverse problems.
Shan, Siming [Yale University, New Haven, CT (Unit↗
Diffusion model approach to simulating electron-proton scattering events
Generative artificial intelligence is a fast-growing area of research offering various avenues for exploration in high-energy nuclear physics. In this work, we explore the use of generative models for simulating electron-proton collisions relevant to experiments like the Continuous Electron Beam Accelerator Facility and the future Electron-Ion Collider (EIC). These experiments play a critical role in advancing our understanding of nucleons and nuclei in terms of quark and gluon degrees of freedom. The use of generative models for simulating collider events faces several challenges such as the sparsity of the data, the presence of global or eventwide constraints, and steeply falling particle distributions. In this work, we focus on the implementation of diffusion models for the simulation of electron-proton scattering events at EIC energies. Our results demonstrate that diffusion models can reproduce relevant observables such as momentum distributions and correlations of particles, momentum sum rules, and the leading electron kinematics, all of which are of particular interest in electron-proton collisions. Although the sampling process is relatively slow compared to other machine-learning architectures, we find diffusion models can generate high-quality samples. We foresee various applications of our work including inference for nuclear structure, interpretable generative machine learning, and searches of physics beyond the Standard Model. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA/MSFC multilayer diffusion models and computer program for operational prediction of toxic fuel hazards
The NASA/MSFC multilayer diffusion models are discribed which are used in applying meteorological information to the estimation of toxic fuel hazards resulting from the launch of rocket vehicle and from accidental cold spills and leaks of toxic fuels. Background information, definitions of terms, description of the multilayer concept are presented along with formulas for determining the buoyant rise of hot exhaust clouds or plumes from conflagrations, and descriptions of the multilayer diffusion models. A brief description of the computer program is given, and sample problems and their solutions are included. Derivations of the cloud rise formulas, users instructions, and computer program output lists are also included.
Dumbauld, R. K.↗
Accelerating Multiphase Simulations With Denoising Diffusion Model Driven Initializations
This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics‐based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical properties of interest. Pore‐scale simulations enhance our understanding of applications such as assessing hydrogen and storage efficiency in underground reservoirs. Nevertheless, they are computationally expensive and the presence of non‐unique solutions can require multiple simulations within a single geometry. To overcome the computational cost hurdle, we propose a method that couples generative diffusion models and physics‐based simulations. While training the data‐driven model, we simultaneously generate initial conditions and perform physics‐based simulations using these. This integrated approach enables us to receive real‐time feedback on a single compute node equipped with both CPUs and GPUs. By efficiently managing these processes within a single compute node, we can continuously monitor performance and halt training once the model meets the specified criteria. To test our model, we generate realizations in a real Berea sandstone fracture which shows that our technique is up to 4.4 times faster than commonly used flow simulation initializations.
36 MATERIALS SCIENCE↗
A reaction–diffusion model for phenotypic evolution
We present a reaction–diffusion mathematical model for the evolutionary dynamics of phenotypic evolution. A detailed deduction of the equations is presented for the one-dimensional version, from which a more general model is proposed. Particular cases are studied using analytical approximations and numerical simulations. Results indicate that the approach proposed produces results that are coherent with mainstream models in evolutionary dynamics, suggesting that the reaction–diffusion model could be an alternative tool in the analysis of evolutionary dynamics.
97 MATHEMATICS AND COMPUTING↗
Investigations into a diffusion model of dry heat sterilization Interim report
Diffusion model of dry heat sterilization
Barrett, M. J.↗
Rise and growth of space vehicle engine exhaust and associated diffusion models
Space vehicle plume rise and associated diffusion models at Cape Kennedy Launch Complex
Chandler, M. W.↗
A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions
In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.
97 MATHEMATICS AND COMPUTING↗
Simulation of Ultra-Small MOSFETs Using a 2-D Quantum-Corrected Drift-Diffusion Model
The continued down-scaling of electronic devices, in particular the commercially dominant MOSFET, will force a fundamental change in the process of new electronics technology development in the next five to ten years. The cost of developing new technology generations is soaring along with the price of new fabrication facilities, even as competitive pressure intensifies to bring this new technology to market faster than ever before. To reduce cost and time to market, device simulation must become a more fundamental, indeed dominant, part of the technology development cycle. In order to produce these benefits, simulation accuracy must improve markedly. At the same time, device physics will become more complex, with the rapid increase in various small-geometry and quantum effects. This work describes both an approach to device simulator development and a physical model which advance the effort to meet the tremendous electronic device simulation challenge described above. The device simulation approach is to specify the physical model at a high level to a general-purpose (but highly efficient) partial differential equation solver (in this case PROPHET, developed by Lucent Technologies), which then simulates the model in 1-D, 2-D, or 3-D for a specified device and test regime. This approach allows for the rapid investigation of a wide range of device models and effects, which is certainly essential for device simulation to catch up with, and then stay ahead of, electronic device technology of the present and future. The physical device model used in this work is the density-gradient (DG) quantum correction to the drift-diffusion model [Ancona, Phys. Rev. B 35(5), 7959 (1987)]. This model adds tunneling and quantum smoothing of carrier density profiles to the drift-diffusion model. We used the DG model in 1-D and 2-D (for the first time) to simulate both bipolar and unipolar devices. Simulations of heavily-doped, short-base diodes indicated that the DG quantum corrections do not have a large effect on the IN characteristics of electronic devices without heteroj unction s. On the other hand, ultra-small MOSFETs certainly exhibit important quantum effects that the DG model will include: quantum repulsion of the inversion and gate charges from the oxide interfaces, and quantum tunneling through thin gate oxides. We present initial results of 2-D DG simulations of ultra-small MOSFETs. Subtle but important issues involving the specification of the model, boundary conditions, and interface constraints for DG simulation of MOSFETs will also be illuminated.
Biegal, Bryan A.↗
Application of a unidimensional diffusion model to the propagation of solar cosmic rays
Unidimensional diffusion model for solar cosmic ray propagation within bounded layer
PARTICLE DIFFUSION↗