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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Monte Carlo Simulation and Reconstruction: Assessment of Myocardial Perfusion Imaging of Tracer Dynamics With Cardiac Motion Due to Deformation and Respiration Using Gamma Camera With Continuous Acquisition

Purpose: Myocardial perfusion imaging (MPI) with single photon emission computed tomography (SPECT) is routinely used for stress testing in nuclear medicine. Recently, our group extended its potential going from 3D visual qualitative image analysis to 4D spatiotemporal reconstruction of dynamically acquired data to capture the time variation of the radiotracer concentration and the estimated myocardial blood flow (MBF) and coronary flow reserve (CFR). However, the quality of reconstructed image is compromised due to cardiac deformation and respiration. The work presented here develops an algorithm that reconstructs the dynamic sequence of separate respiratory and cardiac phases and evaluates the algorithm with data simulated with a Monte Carlo simulation for the continuous image acquisition and processing with a slowly rotating SPECT camera. Methods: A clinically realistic Monte Carlo (MC) simulation is developed using the 4D Extended Cardiac Torso (XCAT) digital phantom with respiratory and cardiac motion to model continuous data acquisition of dynamic cardiac SPECT with slowly rotating gamma cameras by incorporating deformation and displacement of the myocardium due to cardiac and respiratory motion. We extended our previously developed 4D maximum-likelihood expectation-maximization (MLEM) reconstruction algorithm for a data set binned from a continuous list mode (LM) simulation with cardiac and respiratory information. Our spatiotemporal image reconstruction uses splines to explicitly model the temporal change of the tracer for each cardiac and respiratory gate that delineates the myocardial spatial position as the tracer washes in and out. Unlike in a fully list-mode data acquisition and reconstruction the accumulated photons are binned over a specific but very short time interval corresponding to each cardiac and respiratory gate. Reconstruction results are presented showing the dynamics of the tracer in the myocardium as it continuously deforms. These results are then compared with the conventional 4D spatiotemporal reconstruction method that models only the temporal changes of the tracer activity. Mean Stabilized Activity (MSA), signal to noise ratio (SNR) and Bias for the myocardium activities for three different target-to-background ratios (TBRs) are evaluated. Dynamic quantitative indices such as wash-in (K1) and wash-out (k2) rates at each gate were also estimated. Results: The MSA and SNR are higher with higher TBRs while biases were improved with higher TBRs to less than 10%. The correlation between exhalation-inhalation sequence with the ground truth during respiratory cycle was excellent. Our reconstruction method showed better resolved myocardial walls during diastole to systole as compared to the ungated 4D image. Estimated values of K1 and k2 were also consistent with the ground truth. Conclusion: The continuous image acquisition for dynamic scan using conventional two-head gamma cameras can provide valuable information for MPI. Our study demonstrated the viability of using a continuous image acquisition method on a widely used clinical two-head SPECT system. Our reconstruction method showed better resolved myocardial walls during diastole to systole as compared to the ungated 4D image. Precise implementation of reconstruction algorithms, better segmentation techniques by generating images of different tissue types and background activity would improve the feasibility of the method in real clinical environment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

POINT-SPREAD FUNCTIONS FOR THE EXTREME-ULTRAVIOLET CHANNELS OF SDO/AIA TELESCOPES

We present the stray-light point-spread functions (PSFs) and their inverses we characterized for the Atmospheric Imaging Assembly (AIA) EUV telescopes on board the Solar Dynamics Observatory (SDO) spacecraft. The inverse kernels are approximate inverses under convolution. Convolving the original Level 1 images with them produces images with improved stray-light characteristics. We demonstrate the usefulness of these PSFs by applying them to two specific cases: photometry and differential emission measure (DEM) analysis. The PSFs consist of a narrow Gaussian core, a diffraction component, and a diffuse component represented by the sum of a Gaussian-truncated Lorentzian and a shoulder Gaussian. We determined the diffraction term using the measured geometry of the diffraction pattern identified in flare images and the theoretically computed intensities of the principal maxima of the first few diffraction orders. To determine the diffuse component, we fitted its parameterized model using iterative forward-modeling of the lunar interior in the SDO/AIA images from the 2011 March 4 lunar transit. We find that deconvolution significantly improves the contrast in dark features such as miniature coronal holes, though the effect was marginal in bright features. On a percentage-scattering basis, the PSFs for SDO/AIA are better by a factor of two than that of the EUV telescope on board the Transition Region And Coronal Explorer mission. A preliminary analysis suggests that deconvolution alone does not affect DEM analysis of small coronal loop segments with suitable background subtraction. We include the derived PSFs and their inverses as supplementary digital materials.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Development of Integrated Safety and Security Models for Comprehensive Reliability and Resiliency Evaluation

The security of the electric grid and supporting energy systems is crucial to national security. One of the complexities in analyzing the security of energy systems is the safety consequences that may result from accidents. For energy systems, the goal is to ensure that they operate as intended and that any consequences are mitigated or prevented. The integration of safety and security is paramount to protecting these systems from attacks and ensuring that large consequences are prevented. This report describes an integrated safety and security methodology to evaluate cybersecurity events that can lead to large consequences. This novel approach first describes how Systems-Theoretic Process Analysis (STPA) provides a digital causal analysis for Bayesian Networks (BNs). The use of STPA causal analysis provides a systematic approach to constructing BNs that adequately model cyber scenarios that result in consequences. When combined with the technical principles described in Risk-Informed Management of Enterprise Systems (RIMES), a comprehensive risk-informed cybersecurity analysis results that allows decision-makers to prioritize systems that most impact risk.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Seventy-five years of nuclear criticality safety documents - a bibliography

A collection of nuclear criticality documents was begun in the 1970's at the University of California's Lawrence Livermore Laboratory (now Lawrence Livermore National Laboratory). Documents in this bibliography are dated as early as 1940. The early documents described experimental work that was of vital importance to the safe use of fissile materials at nuclear reactors, the facilities for preparing or transporting nuclear fuel, or its eventual storage. The experiments were of direct value to support safe operations with fissile materials but they were also needed for validating early physics data and calculational methods and then for validating computational methods used in criticality safety evaluations. These documents provided information for our computerized bibliographic database. The bibliography was originally intended for use by Livermore staff members but criticality safety 'pioneers' encouraged us to make the database available to the broader nuclear safety community and even shared copies of their bibliographies and reports. A publication of the bibliography is being prepared and a searchable database is available on the U.S. Department of Energy's Nuclear Criticality Safety Program's NCSP web site. The NCSP web site also includes links from the bibliography to many full-text documents. The database continues to expand--the information in this paper is based on a 'snapshot' of its present status. The 'vintage' hardcopy document collection is preserved and is being scanned into digital format. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Protonic nickelate device networks for spatiotemporal neuromorphic computing

Computation in biological neural circuits arises from the interplay of nonlinear temporal responses and spatially distributed dynamic network interactions. Replicating this richness in hardware has remained challenging, as most neuromorphic devices emulate only isolated neuron- or synapse-like functions. Here we introduce an integrated neuromorphic computing platform in which both nonlinear spatiotemporal processing and programmable memory are realized within a single perovskite nickelate material system. By engineering symmetric and asymmetric hydrogenated NdNiO 3 junction devices on the same wafer, we combine ultrafast, proton-mediated transient dynamics with stable multilevel resistance states. Networks of symmetric NdNiO 3 junctions exhibit emergent spatial interactions mediated by proton redistribution, while each node simultaneously provides short-term temporal memory, enabling nanosecond-scale operation with an energy cost of ~0.2 nJ per input. When interfaced with asymmetric output units serving as reconfigurable long-term weights, these networks allow both feature transformation and linear classification in the same material system. Leveraging these emergent interactions, the platform enables real-time pattern recognition and achieves high accuracy in spoken digit classification and early seizure detection, outperforming temporal-only or uncoupled architectures. These results position protonic nickelates as a compact, energy-efficient, CMOS-compatible platform that integrates processing and memory for scalable intelligent hardware.

Electrical and electronic engineering↗
DOE OSTI2020

Flat optics for image differentiation

Image processing has become a critical technology in a variety of science and engineering disciplines. Although most image processing is performed digitally, optical analog processing has the advantages of being low-power and high-speed, but it requires a large volume. Here, we demonstrate flat optics for direct image differentiation, allowing us to significantly shrink the required optical system size. We first demonstrate how the differentiator can be combined with traditional imaging systems such as a commercial optical microscope and camera sensor for edge detection with a numerical aperture up to 0.32. We next demonstrate how the entire processing system can be realized as a monolithic compound flat optic by integrating the differentiator with a metalens. The compound nanophotonic system manifests the advantage of thin form factor as well as the ability to implement complex transfer functions, and could open new opportunities in applications such as biological imaging and computer vision.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Quantum JPEG

The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Development of a Data Acquisition System for Kinetic Inductance Detectors: Wide Dynamic Range and High Sampling Rate for Astronomical Observation

Microwave kinetic inductance detectors have a variety of potential applications in astronomical observations. We built a data acquisition system for kinetic inductance detectors combining a dedicated analog board and a commercially available digital board to meet the requirements of astronomical measurements, such as observation of the cosmic microwave background. This paper reports the status of the development of the data acquisition system. We have already achieved simultaneous readout through 120 channels using a direct down-conversion method to decode the signal. A variety of software has been developed and tested using the functionalities of the system and actual detectors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Polynomial-time preparation of low-temperature Gibbs states for two-dimensional toric code

In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A Four Channel Beam Current Monitor Data Acquisition System Using Embedded Processors

Data acquisition from multiple beam current monitors is required for electron accelerator production of Mo-99. A two channel system capable of recording data from two beam current monitors has been developed, is currently in use, and is discussed below. The development of a cost-effective method of extending this system to more than two channels and integrating of these measurements into an accelerator control system is the main focus of this report. Data from these current monitors is digitized, processed, and stored by a digital data acquisition system. Limitations and drawbacks with the currently deployed digital data acquisition system have been identified as have been potential solutions, or at least improvements, to these problems. This report will discuss and document the efforts we've made in improving the flexibility and lowering the cost of the data acquisition system while maintaining the minimum requirements.

42 ENGINEERING↗
DOE OSTI2019

A Domain-Specific Language for High-Consequence Control Software

While most software development for control systems is directed at what the system is supposed to do (i.e., function), high-consequence controls must account for what the system is not supposed to do (i.e., safety, security and reliability requirements). A Domain Specific Language (DSL) for high-consequence digital controls is proposed. As with similar tools for the design of controls, the DSL will have plug-in modules for common controller functions. However, the DSL will also augment these modules with attendant "templates" that aid in the proof of safety, security and reliability requirements, not available in current tools. The object is to create a development methodology that makes construction of high-assurance control systems as easy as controls that are designed for function alone.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advanced Reactor Safeguards & Security Program: Cybersecurity Scenarios

The use of digital control systems and automation in advanced nuclear power systems introduces different types of vulnerabilities compared to legacy (i.e. analog) control systems that cyber adversaries can exploit. These vulnerabilities pose a challenge to reactor operators and cyber operations staff due to the dynamic nature of the event in which a human response or a lack of response can potentially evolve into a worsening plant condition. Using the Department of Homeland Security Cyber and Infrastructure Security Agency’s (CISA) critical infrastructure exercise framework, this document presents several cyber security scenarios typical of digital control systems that could be used in advanced reactor designs. These scenarios can be used in tabletop exercises to evaluate cyber security posture or conduct training on different aspects of cyber security, including detection, threat hunting using indicators of compromise, evaluating incident response, risk mitigation, incident reporting, information sharing and recovery.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

THE FAINT END OF THE LUMINOSITY FUNCTION AND LOW SURFACE BRIGHTNESS GALAXIES

Smithsonian Hectospec Lensing Survey (SHELS) is a dense redshift survey covering a 4 deg{sup 2} region to a limiting R = 20.6. In the construction of the galaxy catalog and in the acquisition of spectroscopic targets, we paid careful attention to the survey completeness for lower surface brightness dwarf galaxies. Thus, although the survey covers a small area, it is a robust basis for computation of the slope of the faint end of the galaxy luminosity function to a limiting M{sub R} = -13.3 + 5log h. We calculate the faint-end slope in the R band for the subset of SHELS galaxies with redshifts in the range 0.02 {<=}z < 0.1, SHELS{sub 0.1}. This sample contains 532 galaxies with R < 20.6 and with a median surface brightness within the half-light radius of SB{sub 50,R} = 21.82 mag arcsec{sup -2}. We used this sample to make one of the few direct measurements of the dependence of the faint end of the galaxy luminosity function on surface brightness. For the sample as a whole the faint-end slope, {alpha} = -1.31 {+-} 0.04, is consistent with both the Blanton et al. analysis of the Sloan Digital Sky Survey and the Liu et al. analysis of the COSMOS field. This consistency is impressive given the very different approaches of these three surveys. A magnitude-limited sample of 135 galaxies with optical spectroscopic redshifts with mean half-light surface brightness, SB{sub 50,R} {>=} 22.5 mag arcsec{sup -2} is unique to SHELS{sub 0.1}. The faint-end slope is {alpha}{sub 22.5} = -1.52 {+-} 0.16. SHELS{sub 0.1} shows that lower surface brightness objects dominate the faint-end slope of the luminosity function in the field, underscoring the importance of surface brightness limits in evaluating measurements of the faint-end slope and its evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Dosimetric characterization and organ dose assessment in digital breast tomosynthesis: Measurements and Monte Carlo simulations using voxel phantoms

Purpose: Due to its capability to more accurately detect deep lesions inside the breast by removing the effect of overlying anatomy, digital breast tomosynthesis (DBT) has the potential to replace the standard mammography technique in clinical screening exams. However, the European Guidelines for DBT dosimetry are still a work in progress and there are little data available on organ doses other than to the breast. It is, therefore, of great importance to assess the dosimetric performance of DBT with respect to the one obtained with standard digital mammography (DM) systems. The aim of this work is twofold: (i) to study the dosimetric properties of a combined DBT/DM system (MAMMOMAT Inspiration Siemens{sup ®}) for a tungsten/rhodium (W/Rh) anode/filter combination and (ii) to evaluate organs doses during a DBT examination. Methods: For the first task, measurements were performed in manual and automatic exposure control (AEC) modes, using two homogeneous breast phantoms: a PMMA slab phantom and a 4 cm thick breast-shaped rigid phantom, with 50% of glandular tissue in its composition. Monte Carlo (MC) simulations were performed using Monte Carlo N-Particle eXtended v.2.7.0. A MC model was implemented to mimic DM and DBT acquisitions for a wide range of x-ray spectra (24 –34 kV). This was used to calculate mean glandular dose (MGD) and to compute series of backscatter factors (BSFs) that could be inserted into the DBT dosimetric formalism proposed by Dance et al. Regarding the second aim of the study, the implemented MC model of the clinical equipment, together with a female voxel phantom (“Laura”), was used to calculate organ doses considering a typical DBT acquisition. Results were compared with a standard two-view mammography craniocaudal (CC) acquisition. Results: Considering the AEC mode, the acquisition of a single CC view results in a MGD ranging from 0.53 ± 0.07 mGy to 2.41 ± 0.31 mGy in DM mode and from 0.77 ± 0.11 mGy to 2.28 ± 0.32 mGy in DBT mode. Regarding the BSF, the results achieved may lead to a MGD correction of about 6%, contributing to the improvement of the current guidelines used in these applications. Finally, considering the MC results obtained for the organ dose study, the radiation doses found for the tissues of the body other than the breast were in the range of tens of μSv, and are in part comparable to the ones obtained in standard DM. Nevertheless, in a single DBT examination, some organs (such as lung and thyroid) receive higher doses (of about 9% and 21%, respectively) with respect to the CC DM acquisition. Conclusions: Taking into account an average breast with a thickness of 4.5 cm, the MGDs for DM and DBT acquisitions were below the achievable value (2.0 mGy) defined by the European protocol. Additionally, in the case of a fusion imaging study (DM + DBT), the MGD for a 4.5 cm thick breast is of the order of 1.88 ± 0.36 mGy. Finally, organ dose evaluations underline the need to improve awareness concerning dose estimation of DBT exams for some organs, especially when radiation risk is assessed by using the effective dose.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Emerging Technologies in the Built Environment: Geographic Information Science (GIS), 3D Printing, and Additive Manufacturing

Abstract 1: Geographic information systems emerged as a computer application in the late 1960s, led in part by projects at ORNL. The concept of a GIS has shifted through time in response to new applications and new technologies, and is now part of a much larger world of geospatial technology. This presentation discusses the relationship of GIS and estimating hourly and seasonal energy consumption profiles in the building sector at spatial scales down to the individual parcel. The method combines annual building energy simulations for city-specific prototypical buildings and commonly available geospatial data in a GIS framework. Abstract 2: This presentation focuses on 3D printing technologies and how they have rapidly evolved over the past couple of years. At a basic level, 3D printing produces physical models quickly and easily from 3D CAD, BIM (Building Information Models), and other digital data. Many AEC firms have adopted 3D printing as part of commercial building design development and project delivery. This presentation includes an overview of 3D printing, discusses its current use in building design, and talks about its future in relation to the HVAC industry. Abstract 3: This presentation discusses additive manufacturing and how it is revolutionizing the design of commercial and residential facilities. Additive manufacturing utilizes a broad range of direct manufacturing technologies, including electron beam melting, ultrasonic, extrusion, and laser metal deposition for rapid prototyping. While there is some overlap with the 3D printing talk, this presentation focuses on the materials aspect of additive manufacturing and also some of the more advanced technologies involved with rapid prototyping. These technologies include design of carbon fiber composites, lightweight metals processing, transient field processing, and more.

New, Joshua Ryan↗
DOE OSTI2019

Pulse Pileup Analysis for a Double-Sided Silicon Strip Detector Using Variable Pulse Shapes

On account of pulse pileup, photon counting detectors (PCDs) suffer from count loss and energy distortion when operating in high count rate environments. Here, we researched the pulse pileup of a double-sided silicon strip detector (DSSSD) to evaluate its potential application in a mammography system. We analyzed the pulse pileup using pulses of varied shapes, where the shape of the pulse depends on the location of photon interaction within the detector. To obtain the shaped pulses, first, transient currents for photons interacting at different locations were simulated using a Technology Computer-Aided Design (TCAD) software. Next, the currents were shaped by a CR- RC 2 shaping circuit, calculated using Simulink. After obtaining these pulses, both the different orders of pileup and the energy spectrum were calculated by taking into account the following two factors: 1) spatial distribution of photon interactions within the detector and 2) time interval distribution between successive photons under a given photon flux. We found that for a DSSSD with a thickness of 300 μm, a pitch of 25 μm, and a strip length of 1 cm, under a bias voltage of 50 V, the variable pulse shape model predicts that the fraction free of pileup can be >90% under a photon flux of 3.75 Mcps/mm 2 (million counts per second per square mm). The DSSSD is a promising candidate for digital mammography applications.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Patient motion effects on the quantification of regional myocardial blood flow with dynamic PET imaging

Purpose: Patient motion is a common problem during dynamic positron emission tomography (PET) scans for quantification of myocardial blood flow (MBF). The purpose of this study was to quantify the prevalence of body motion in a clinical setting and evaluate with realistic phantoms the effects of motion on blood flow quantification, including CT attenuation correction (CTAC) artifacts that result from PET–CT misalignment. Methods: A cohort of 236 sequential patients was analyzed for patient motion under resting and peak stress conditions by two independent observers. The presence of motion, affected time-frames, and direction of motion was recorded; discrepancy between observers was resolved by consensus review. Based on these results, patient body motion effects on MBF quantification were characterized using the digital NURBS-based cardiac-torso phantom, with characteristic time activity curves (TACs) assigned to the heart wall (myocardium) and blood regions. Simulated projection data were corrected for attenuation and reconstructed using filtered back-projection. All simulations were performed without noise added, and a single CT image was used for attenuation correction and aligned to the early- or late-frame PET images. Results: In the patient cohort, mild motion of 0.5 ± 0.1 cm occurred in 24% and moderate motion of 1.0 ± 0.3 cm occurred in 38% of patients. Motion in the superior/inferior direction accounted for 45% of all detected motion, with 30% in the superior direction. Anterior/posterior motion was predominant (29%) in the posterior direction. Left/right motion occurred in 24% of cases, with similar proportions in the left and right directions. Computer simulation studies indicated that errors in MBF can approach 500% for scans with severe patient motion (up to 2 cm). The largest errors occurred when the heart wall was shifted left toward the adjacent lung region, resulting in a severe undercorrection for attenuation of the heart wall. Simulations also indicated that the magnitude of MBF errors resulting from motion in the superior/inferior and anterior/posterior directions was similar (up to 250%). Body motion effects were more detrimental for higher resolution PET imaging (2 vs 10 mm full-width at half-maximum), and for motion occurring during the mid-to-late time-frames. Motion correction of the reconstructed dynamic image series resulted in significant reduction in MBF errors, but did not account for the residual PET–CTAC misalignment artifacts. MBF bias was reduced further using global partial-volume correction, and using dynamic alignment of the PET projection data to the CT scan for accurate attenuation correction during image reconstruction. Conclusions: Patient body motion can produce MBF estimation errors up to 500%. To reduce these errors, new motion correction algorithms must be effective in identifying motion in the left/right direction, and in the mid-to-late time-frames, since these conditions produce the largest errors in MBF, particularly for high resolution PET imaging. Ideally, motion correction should be done before or during image reconstruction to eliminate PET-CTAC misalignment artifacts.

60 APPLIED LIFE SCIENCES↗
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↗