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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

Although current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build-up to detonation, a new paradigm is put forth for modelling sub-grid, reaction-induced fluctuations (i.e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin-type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i.e. deterministic) and diffusion (i.e. stochastic) coefficients. Furthermore, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave-like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no-go estimation (e.g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i.e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Hence, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub-grid stochastic behaviour of shocked heterogeneous solid explosives.

42 ENGINEERING↗
DOE OSTI2021

Stochastic evaluation of fourth-order many-body perturbation energies

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green’s functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n 5.3 ) size-dependence of cost, which is nearly two ranks lower than the O(n 7 ) dependence of the deterministic MP4 algorithm. Furthermore, it evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE h (1.1% of the total basis-set correlation energy), 38 mE h (2.6%), 110 mE h (5.5%), and 280 mE h (9.0%), respectively, after about 10 9 MC steps.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Chaotic vortex filaments in a Bose – Einstein condensate and in superfluid helium

A statement of the quantum turbulence problem in both a Bose – Einstein condensate (BEC) and superfluid helium is formulated. In superfluid helium use is made of a so-called vortex filament method, in which quantum vortices are represented by string-like objects, i.e. vortex lines. The dynamics of the vortex lines is determined by deterministic equations of motion, supplemented by random reconnections. Unlike He II, the laws of the dynamics of quantum vortices in BEC are based on the nonlinear Schrödinger equation. This makes it possible to obtain a microscopic description of the collision of vortices, the structure of a vortex filament, etc. A comparative analysis of these complementary approaches is carried out. It is shown that there are some features that do not automatically transfer the results obtained for BEC to vortices in He II and vice versa. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Radiological Performance Modeling: Platform Comparison

Zapadnoe Uranium Mill Tailings Site, Pridneprovsky Chemical Plant Ukraine: Two exposure scenarios were utilized to develop performance assessment models in GoldSim and NORMALYSA. The first scenario is an onsite worker exposed to radioactivity through external ground irradiation as well as radon and radioactive dust inhalation. The second being an offsite Resident 300 years after institutional control exposed through the ingestion of garden vegetables irrigated by contaminated ground water, ingestion of fish from Konoplyanka River, and agricultural activities in contaminated garden. NORMALYSA utilizes a modular interface to connect extensive pre-created modules to develop contaminant transport and risk assessment models for safety assessments and performance assessments at NORM and legacy sites. Developed by Facilia AB, the program was tested with the creation of the Zapadnoe model under the International Atomic Energy Agency MODARIA Il Working Group 1 (WG1). Default values are provided for input parameters where site specific data and distributions lack. Probabilistic simulations and inputs are limited to parameters with assigned Gaussian probability functions. Similar results for transient worker inhalation dose were found in comparison with the Zapadnoe GoldSim model. However, the NORMALYSA model has results larger by an order of magnitude for external radiation in the transient worker and for aquatic food ingestion, inhalation, and garden food ingestion to the resident. Performance Assessment Modeling: Radiological performance models promote good management and support in remediation and environmental decision making by optimizing radioactive waste disposal site performance. a performance assessment model of the Zapadnoe uranium mill tailings site and a model for calculating authorized limits at Los Alamos National Laboratory are created to demonstrate and highlight the respective capabilities of three modeling platforms: GoldSim, NORMALYSA, and RESRAD-Onsite. GoldSim is a general-purpose modeling platform with the ability to simulate site-specific FT radionuclide transport and risk assessment using a graphical interface to create and link elements that act as indivisible building blocks of the model. The Zapadnoe performance assessment model created in GoldSim is composed of input parameters collected from site specific parameters from WG1 as well as standard assumptions seen in the Generic PA Model from Neptune and Company. The multivariate Zapadnoe simulation contains both deterministic and probabilistic simulation capabilities with the ability to quantitatively represent the uncertainty and associated risks of the site via the Monte Carlo simulation method. Model parameters, documentation, and assumptions are built directly into the model creating a transparent, reproducible, and more purposeful site specific model. To demonstrate this, an ingestion of water pathway was included in addition to the exposure pathways included in the NORMALYSA model. GoldSim offers a wide variety of probability distributions to choose from as well as many tools to visualize the uncertainty of the models and explore which pathways and radionuclides dominate dose. In contrast to the NORMALYSA model, the GoldSim model uses dynamic simulation to calculate tritium concentrations. Authorized limits support the evaluation of radiological health effects from radionuclides present in bulk contaminated soil in order to assist in the process of clearing land for release under different uses. Calculations of authorized limits in RESRAD-Onsite and GoldSim models support the evaluation for 15 radionuclides using a residential exposure scenario, indoor and outdoor inhalation of dust and vapor phase radionuclides (tritium), incidental soil ingestion, and ingestion grown fruits and Vegetables. RESRAD-Onsite, developed by Argonne National Laboratory is a dedicated computer code for calculating radiation doses and cancer risks to an individual located on top of radioactively contaminated soils. It can also be used to provide guidelines for deriving radionuclide soil levels corresponding to a specific dose criterion. The menu driven user interface facilitates selection of radionuclides and soil concentrations, as well as defines parameter values related to materials, environmental factors, and exposure pathways. The program contains radionuclide-specific data such as dose conversion factors and risk coefficients, as well as soil-water partition coefficients and transfer factors for biotic media. The GoldSim model successfully emulates the RESRAD-Onsite code using identical radiological decay and ingrowth factors, radiation dose conversion factors, and other input parameters. DE EEDE ETS Each model supports dynamic modeling of radionuclide ingrowth and decay over time, and integrate this capability with the transport of radionuclides in the environment via processes such as advection and/or diffusion in fluids, or within porous solid media, The applicability of each program is heavily dependent on project context. In the context of developing Authorized Limits, RESRAD-Onsite may be a more desirable option as it was developed for this particular application. For simple disposal or legacy sites or sites that do not need site-specific model structure, NORMALYSA may be a desirable modeling platform, GoldSim can be used to model any problem for which RESRAD or NORMALYSA is applicable, but its strength lies in its flexibility, analytical, and probabilistic capabilities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Limitations of Hartree–Fock with quantum resources

The Hartree–Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the Hartree–Fock method, central to many other numerical approaches, is a natural target for quantum enhanced algorithms. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the non-deterministic polynomial-complete Hartree–Fock problem is not a likely candidate. Here, we highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of energy landscapes for simple systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Computational study of Fermi kinetics transport applied to large-signal RF device simulations

Here, a detailed description and analysis of the Fermi kinetics transport (FKT) equations for simulating charge transport in semiconductor devices is presented. The fully coupled nonlinear discrete FKT equations are elaborated, as well as solution methods and work-flow for the simulation of RF electronic devices under large-signal conditions. The importance of full-wave electromagnetics is discussed in the context of high-speed device simulation, and the meshing requirements to integrate the full-wave solver with the transport equations are given in detail. The method includes full semiconductor band structure effects to capture the scattering details for the Boltzmann transport equation. The method is applied to high-speed gallium nitride devices. Finally, numerical convergence and stability examples provide insight into the mesh convergence behavior of the deterministic solver.

42 ENGINEERING↗
DOE OSTI2020

Uncertainty Quantification in Atomistic Modeling of Metals and Its Effect on Mesoscale and Continuum Modeling: A Review

The design of next-generation alloys through the integrated computational materials engineering (ICME) approach relies on multiscale computer simulations to provide thermodynamic properties when experiments are difficult to conduct. Atomistic methods such as density functional theory (DFT) and molecular dynamics (MD) have been successful in predicting properties of never before studied compounds or phases. However, uncertainty quantification (UQ) of DFT and MD results is rarely reported due to computational and UQ methodology challenges. Over the past decade, studies that mitigate this gap have emerged. These advances are reviewed in the context of thermodynamic modeling and information exchange with mesoscale methods such as the phase-field method (PFM) and calculation of phase diagrams (CALPHAD). The importance of UQ is illustrated using properties of metals, with aluminum as an example, and highlighting deterministic, frequentist, and Bayesian methodologies. Finally, challenges facing routine uncertainty quantification and an outlook on addressing them are also presented.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A deterministic gradient-based approach to avoid saddle points

Abstract Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317 ], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is $\lfloor (n-1)/2\rfloor$ , and hence it is significantly smaller than that of GD whose dimension is $n-1$ .

Mathematics↗
DOE OSTI2020

Temperature drives local contributions to beta diversity in mountain streams: stochastic and deterministic processes

Community variation (i.e. beta diversity) in geographical coenoclines is of substantial interest in ecology, yet the elevational patterns in beta diversity are still understudied, and no general conclusions have been reached. Here, we explored local contributions to beta diversity (LCBD) of stream bacteria, diatoms and macroinvertebrates on mountainsides. Across all taxa, we revealed a general U-shaped LCBD-elevation relationships (LCBDer), suggesting higher uniqueness of community composition at the two ends of the elevational gradients. This pattern was confirmed by coenocline simulations based on observed communities, and supported by the dominance of species replacement in total beta diversity. Across mountains and taxonomic groups, temperature was the main environmental factor underlying elevational patterns in LCBD and its metric relatives, which were also mediated by local environmental variables. The observed magnitudes of U-shaped LCBDer across mountains and taxonomic groups were specifically related to the heterogeneity of stream morphology, and the mean annual temperature on each mountain. U-shaped LCBDer were strengthened by the occurrence of generalist species with large elevational ranges, while rare species had a lesser effect on the patterns. Raup-Crick beta diversity indicated that both stochastic and deterministic processes drove the community assembly, and the latter one was positively related to the magnitudes of LCBDer. Our synthesis across mountains and taxonomic groups clearly shows that there are consistent elevational patterns in LCBD among taxonomic groups, and that these patterns are explained by similar ecological mechanisms, producing a more complete picture in understanding and bridging the spatial variation in biodiversity under changing climate.

Wang, Jianjun↗
DOE OSTI2025

Chemical classification program synthesis using generative artificial intelligence

Accurately classifying chemical structures is essential for cheminformatics and bioinformatics, including tasks such as identifying bioactive compounds of interest, screening molecules for toxicity to humans, finding non-organic compounds with desirable material properties, or organizing large chemical libraries for drug discovery or environmental monitoring. However, manual classification is labor-intensive and difficult to scale to large chemical databases. Existing automated approaches either rely on manually constructed classification rules, or are deep learning methods that lack explainability. This work presents an approach that uses generative artificial intelligence to automatically write chemical classifier programs for classes in the Chemical Entities of Biological Interest (ChEBI) database. These programs can be used for efficient deterministic run-time classification of SMILES structures, with natural language explanations. The programs themselves constitute an explainable computable ontological model of chemical class nomenclature, which we call the ChEBI Chemical Class Program Ontology (C3PO). We validated our approach against the ChEBI database, and compared our results against deep learning models and a naive SMARTS pattern based classifier. C3PO outperforms the naive classifier, but does not reach the performance of state of the art deep learning methods. However, C3PO has a number of strengths that complement deep learning methods, including explainability and reduced data dependence. C3PO can be used alongside deep learning classifiers to provide an explanation of the classification, where both methods agree. The programs can be used as part of the ontology development process, and iteratively refined by expert human curators.

Artificial Intelligence↗
DOE OSTI2019

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Inverse regression for ridge recovery: a data-driven approach for parameter reduction in computer experiments

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction (SDR) use data to reduce the predictor dimension of a regression problem. A computational scientist hoping to use SDR for parameter reduction encounters a problem: a computer prediction is best represented by a deterministic function of the inputs, so data comprised of computer simulation queries fail to satisfy the SDR assumptions. To address this problem, here we interpret SDR methods sliced inverse regression (SIR) and sliced average variance estimation (SAVE) as estimating the directions of a ridge function, which is a composition of a low-dimensional linear transformation with a nonlinear function. Within this interpretation, SIR and SAVE estimate matrices of integrals whose column spaces are contained in the ridge directions’ span; we analyze and numerically verify convergence of these column spaces as the number of computer model queries increases. Moreover, we show example functions that are not ridge functions but whose inverse conditional moment matrices are low-rank. Consequently, the computational scientist should beware when using SIR and SAVE for parameter reduction, since SIR and SAVE may mistakenly suggest that truly important directions are unimportant.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in this stochastic economic dispatch problem for forecasting purposes, the conventional Monte-Carlo method is prohibitively time-consuming for practical applications. To overcome this problem, here we propose a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling as the computer experimental design, a Gaussian-process emulator is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated stochastic economic dispatch model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

17 WIND ENERGY↗
DOE OSTI2022

GANISP: A GAN-Assisted Importance Splitting Probability Estimator

Designing manufacturing processes with high yield and strong reliability relies on effective methods for rare event estimation. Genealogical importance splitting reduces the variance of rare event probability estimators by iteratively selecting and replicating realizations that are headed towards a rare event. The replication step is difficult when applied to deterministic systems where the initial conditions of the offspring realizations need to be modified. Typically, a random perturbation is applied to the offspring to differentiate their trajectory from the parent realization. However, this random perturbation strategy may be effective for some systems while failing for others, preventing variance reduction in the probability estimate. This work seeks to address this limitation using a generative model such as a Generative Adversarial Network (GAN) to generate perturbations that are consistent with the attractor of the dynamical system. The proposed GAN-assisted Importance SPlitting method (GANISP) improves the variance reduction for the system targeted. An implementation of the method is available in a companion repository (https://github.com/NREL/GANISP).

generative adversarial network↗
DOE OSTI2020

Reinforcement learning based automated history matching for improved hydrocarbon production forecast

History matching aims to find a numerical reservoir model that can be used to predict the reservoir performance. An engineer and model calibration (data inversion) method are required to adjust various parameters/properties of the numerical model in order to match the reservoir production history. In this study, we develop deep neural networks within the reinforcement learning framework to achieve automated history matching that will reduce engineers’ efforts, human bias, automatically and intelligently explore the parameter space, and remove the need of large set of labeled training data. To that end, a fast-marching-based reservoir simulator is encapsulated as an environment for the proposed reinforcement learning. The deep neural-network-based learning agent interacts with the reservoir simulator within reinforcement learning framework to achieve the automated history matching. Reinforcement learning techniques, such as discrete Deep Q Network and continuous Deep Deterministic Policy Gradients, are used toth, used to train the learning agents. The continuous actions enable the Deep Deterministic Policy Gradients to explore more states at each iteration in a a learning episode; consequently, a better history matching is achieved using this algorithm as compared to Deep Q Network. For simplified dual-target composite reservoir models, the best history-matching performances of the discrete and continuous learning methods in terms of normalized root mean square errors are 0.0447 and 0.0038, respectively. Furthermore, our study shows that continuous action space achieved by the deep deterministic policy gradient drastically outperforms deep Q network.

42 ENGINEERING↗
DOE OSTI2020

Improving operational flexibility of integrated energy system with uncertain renewable generations considering thermal inertia of buildings

Insufficient flexibility in system operation caused by traditional "heat-set" operating modes of combined heat and power (CHP) units in winter heating periods is a key issue that limits renewable energy consumption. In order to reduce the curtailment of renewable energy resources through improving the operational flexibility, a novel optimal scheduling model based on chance-constrained programming (CCP), aiming at minimizing the lowest generation cost, is proposed for a small-scale integrated energy system (IES) with CHP units, thermal power units, renewable generations and representative auxiliary equipments. In this model, due to the uncertainties of renewable generations including wind turbines and photovoltaic units, the probabilistic spinning reserves are supplied in the form of chance-constrained; from the perspective of user experience, a heating load model is built with consideration of heat comfort and inertia in buildings. To solve the model, a solution approach based on sequence operation theory (SOT) is developed, where the original CCP-based scheduling model is tackled into a solvable mixed-integer linear programming (MILP) formulation by converting a chance constraint into its deterministic equivalence class, and thereby is solved via the CPLEX solver. We report the simulation results on the modified IEEE 30-bus system demonstrate that the presented method manages to improve operational flexibility of the IES with uncertain renewable generations by comprehensively leveraging thermal inertia of buildings and different kinds of auxiliary equipments, which provides a fundamental way for promoting renewable energy consumption.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗