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At least 1,027 records · Page 57

Temperature Field Reconstruction of Surfaces Heated Through Radiative Heat Transfer Using Convolutional Neural Networks

Microreactors could play a crucial role in decarbonizing our energy portfolio. However, their development and implementation come with specific challenges, particularly regarding cost. Due to their compact size and the harsh operational environment, collecting real-time data on reactor operation can be challenging. Many probe designs are unable to withstand extreme conditions (e.g., temperature, radiation) in the reactor. In this context, using convolutional neural networks (CNNs) can pave the way for developing a nonintrusive approach that relies solely on ex-core sensors. A well-trained physics-informed CNN can reconstruct the distribution of a given physical quantity over a domain using only a few sensors, allowing us to reconstruct the desired field distribution even in a limited space or complex geometries where a large array of sensors is impractical. In this work, we present the initial steps toward developing a real-time tool for monitoring the thermal behavior of nuclear reactor pressure vessels. Based on an experimental setup, a computational model using the Multiphysics Object-Oriented Simulation Environment (moose) framework was built, where the Ray Tracing and Heat Conduction modules were used to evaluate the temperature distribution over a convex metal surface heated through radiative heat transfer. This metal surface represents a section of a heated nuclear reactor vessel wall. The model also accounts for solid mechanics physics through the moose Solid Mechanics module. In situ experimental data, acquired from a Texas A&M facility, were used to validate the computational model. Part of the data generated by the moose model was used to train the convolutional neural network to reconstruct the vessel wall's outer surface temperature. The CNN generalization was then compared against the experimental and computational data.

Aldeia Machado, Luiz Carlos↗

MODELING AND OPTIMIZATION OF A PCM-BASED OCEAN THERMAL ENERGY HARVESTER FOR POWERING UNMANNED UNDERWATER VEHICLES

As oceans cover over 70% of the planet’s surface, they represent a large reservoir of resources that remained vastly untapped. Uncrewed Underwater Vehicles (UUVs) are becoming key technology for ocean exploration. Ocean thermal gradient is a permanent and reliable energy source that can be used to power UUVs using phase change material (PCM)-based thermal engines. However, the main drawback of this technology is its low conversion efficiency. When using PCM-based thermal engines to power UUVs, there are different energy conversion stages, thermal-hydraulic, hydraulic-kinetic, kinetic-electrical, dependent of a wide variety of parameters. Thus, optimization of the overall energy conversion is still a challenge for powering the increasing energy demanding UUVs for long missions. The goal of this study is to propose a PCM-based ocean thermal energy harvesting system for powering the Solo II float. Using the ocean thermal energy reduces the cost for battery replacement and expands the float’s mission time. For this purpose, we developed a multiphysics model for a system consisting of thermal material, hydraulic, and electrical systems. This system is designed to provide the electrical power needed for the instruments aboard the underwater vehicle. The models of the hydraulic and the electric systems are implemented in MATLAB-Simulink/Simscape environment. The final model developed can provide 13.66 kJ of electrical energy, which is more than 1.5 times the energy requirement per cycle for the SOLO II float.

Ouro-Koura, Habilou↗

Full-System Linearization for Floating Offshore Wind Turbines in OpenFAST

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations (e.g., for design-standards-based loads analysis). Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system properties and exploit well-established methods and tools for analyzing linear systems. This paper presents the development of the new linearization functionality of the open-source engineering tool OpenFAST for floating offshore wind turbines, as well as the concepts and mathematical background needed to understand and apply it.

17 WIND ENERGY↗

SURROGATE MODEL DEVELOPMENT AND VALIDATION FOR RELIABILITY ANALYSIS OF REACTOR PRESSURE VESSELS

In nuclear light water reactors (LWRs), the reactor coolant, core and shroud are contained within a massive, thick walled steel vessel known as a reactor pressure vessel (RPV). Given the tremendous size of these structures, RPVs typically contain a large population of pre-existing flaws introduced in the manufacturing process. After many years of operation, irradiation-induced embrittlement makes these vessels increasingly susceptible to fracture initiation at the locations of the pre-existing flaws. Because of the uncertainty in the loading conditions, flaw characteristics and material properties, probabilistic methods are widely accepted and used in assessing RPV integrity. The Fracture Analysis of Vessels – Oak Ridge (FAVOR) computer program developed by researchers at Oak Ridge National Laboratory is widely used for this purpose. This program can be used in order to perform deterministic and probabilistic risk-informed analyses of the structural integrity of an RPV subjected to a range of thermal-hydraulic events. FAVOR uses a one-dimensional representation of the global response of the RPV, which is appropriate for the beltline region, which experiences the most embrittlement, and employs an influence coefficient technique to rapidly compute stress intensity factors for axis-aligned surface-breaking flaws. The Grizzly code is currently under development at Idaho National Laboratory (INL) to be used as a general multiphysics simulation tool to study a variety of degradation mechanisms in nuclear power plant components. The first application of Grizzly has been to study fracture in embrittled RPVs. Grizzly can be used to model the thermo-mechanical response of an RPV under transient conditions observed in a pressurized thermal shock (PTS) scenario. The global response of the vessel provides boundary conditions for local 3D models of the material in the vicinity of a flaw. Fracture domain integrals are computed to obtain stress intensity factors, which can in turn be used to assess whether a fracture would initiate at a pre-existing flaw. To use Grizzly for probabilistic analysis, it is necessary to have a way to rapidly evaluate stress intensity factors. To accomplish this goal, a reduced order model (ROM) has been developed to efficiently represent the behavior of a detailed 3D Grizzly model used to calculate fracture parameters. This approach uses the stress intensity factor influence coefficient method that has been used with great success in FAVOR. Instead of interpolating between tabulated solutions, as FAVOR does, the ROM approach uses a response surface methodology to compute fracture solutions based on a sampled set of results used to train the ROM. The main advantages of this approach are that the process of generating the training data can be fully automated, and the procedure can be readily used to consider more general flaw configurations. This paper demonstrates the procedure used to generate a ROM to rapidly compute stress intensity factors for axis-aligned flaws. The results from this procedure are in good agreement with those produced using the traditional influence coefficient interpolation procedure, which gives confidence in this method. This paves the way for applying this procedure for more general flaw configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling physical vapor deposition of energetic materials

Morphology and microstructure of organic explosive films formed using physical vapor deposition (PVD) processes strongly depends on local surface temperature during deposition. Currently, there is no accurate means of quantifying the local surface temperature during PVD processes in the deposition chambers. This study focuses on using a multiphysics computational fluid dynamics tool, STARCCM+, to simulate pentaerythritol tetranitrate (PETN) deposition. The PETN vapor and solid phase were simulated using the volume of fluid method and its deposition in the vacuum chamber on spinning silicon wafers was modeled. The model also included the spinning copper cooling block where the wafers are placed along with the chiller operating with forced convection refrigerant. Implicit time-dependent simulations in two- and three-dimensional were performed to derive insights in the governing physics for PETN thin film formation. PETN is deposited at the rate of 14 nm/s at 142.9 °C on a wafer with an initial temperature of 22 °C. The deposition of PETN on the wafers was calculated at an assumed heat transfer coefficient (HTC) of 400 W/m 2 K. This HTC proved to be the most sensitive parameter in determining the local surface temperature during deposition. Previous experimental work found noticeable microstructural changes with 0.5 mm fused silica wafers in place of silicon during the PETN deposition. This work showed that fused silica slows initial wafer cool down and results in ~10 °C difference for the surface temperature at 500 μm PETN film thickness. It was also found that the deposition surface temperature is insensitive to the cooling power of the copper block due to the copper block's very large heat capacity and thermal conductivity relative to the heat input from the PVD process. Future work should incorporate the addition of local stress during PETN deposition. Lastly, based on simulation results, it is also recommended to investigate the impact of wafer surface energy on the PETN microstructure and morphology formation.

36 MATERIALS SCIENCE↗

O · , H · , and · OH radical etching probability of polystyrene obtained for a radio frequency driven atmospheric pressure plasma jet

Atmospheric pressure plasma jets have great potential for the surface modification of polymers. In this work, the authors report on polystyrene etching by a radio frequency driven atmospheric pressure plasma jet with a focus on the role of H · , O · , and · OH radicals in this process. The absolute flux of H · , O · , and · OH radicals reaching the surface of the polymer was determined by a COMSOL MULTIPHYSICS reacting fluid dynamics model incorporating detailed transport phenomena in the boundary layer near the substrate. The simulated results of H · and · OH densities in the jet effluent were experimentally verified by two-photon absorption laser induced fluorescence and laser induced fluorescence, respectively. The carbon atom removal flux from the polystyrene surface was taken from previously reported measurements using the same plasma source. The authors show that the boundary layer effects in the interfacial region above the substrate can have a significant impact on the calculated etching probabilities. The reaction probability (β) has a significant uncertainty although a variation of 2 orders of magnitude in β leads to uncertainties of approximately 1 order of magnitude variation in the determined etching probability. The etching probability of polystyrene by · OH radicals was confirmed to be at least an order of magnitude larger than the polystyrene etching probability by O · radicals. The authors also confirmed the weak polystyrene etching probability by H · radicals. The model suggests that the presence of a 30 ppm O 2 impurity can lead to the production of · OH radicals in the far effluent of the Ar + 1% H 2 plasma jet close to the substrate at sufficient densities to enable effective etching.

36 MATERIALS SCIENCE↗

SU-F-19A-11: Retrospective Evaluation of Thermal Coverage by Thermobrachytherapy Seed Arrangements of Clinical LDR Prostate Implants

Purpose: The superiority of a properly-administered combination of radiation therapy and hyperthermia over radiation alone in treatment of human cancers has been demonstrated in multiple studies examining radiobiology, local control, and survival. Unfortunately, hyperthermia is not yet a common modality in oncology practice, due in part to the technical difficulty of heating a deep-seated target volume to sufficient temperature. To address this problem, our group has invented a thermobrachytherapy (TB) seed based on a commonly-used low dose-rate permanent brachytherapy seed for implant in solid tumors. Instead of the tungsten radiographic marker of the standard seed, the TB seed contains one of a self-regulating ferromagnetic alloy. Placement of a patient implanted with such seeds in an oscillating magnetic field generates heat via induction of eddy currents. We present the results of studies of the capability of clinically-realistic TB seed arrangements to adequately heat defined target volumes. Methods: Seed distributions for several past LDR prostate permanent implant brachytherapy patients were reproduced in the finite element analysis software package COMSOL Multiphysics 4.4, with the difference that TB seeds were modelled, rather than the radiation-only seeds actually used for their treatments. The implant geometries were mainly of the modified peripheral loading type; a range of prostatic volumes and blood perfusion rates likely to be seen in a clinical setting were examined. Results: According to the simulations, when distributed to optimize radiation dose, TB seeds also produce sufficient heat to provide thermal coverage of the target given proper selection of the magnetic field strength. However, the thermal distributions may be improved by additional use of hyperthermia-only seeds. Conclusion: A dual-modality seed intended as an alternative to and using the same implantation apparatus and technique as the standard LDR permanent implant seed has been successfully evaluated for its ability to provide sufficient hyperthermia in clinically-realistic implants. This work was partially supported by the National Institutes of Health (NIH) STTR Grant No. R41 CA153631-01A1.

60 APPLIED LIFE SCIENCES↗

WE-G-17A-08: Electron Gun Operation for in Line MRI-Linac Configurations: An Assessment of Beam Fidelity and Recovery Techniques for Different SIDs and Magnetic Field Strengths

Purpose: To test the functionality of medical electron guns within the fringe field of a purpose built superconducting MRI magnet, and to test different recovery techniques for a variety of imaging field strengths and SIDs. Methods: Three different electron guns were simulated using Finite Element Modelling; a standard diode gun, a standard triode gun, and a novel diode gun designed to operate within parallel magnetic fields. The approximate working regime of each gun was established by assessing exit current in constant magnetic fields of varying strength and defining ‘working’ as less than 10% change in injection current. Next, the 1.0T MRI magnet was simulated within Comsol Multiphysics. The coil currents in this model were also scaled to produce field strengths of .5, 1, 1.5 and 3T. Various magnetic shield configurations were simulated, varying the SID from 800 to 1300mm. The average magnetic field within the gun region was assessed together with the distortion in the imaging volume - greater than 150uT distortion was considered unacceptable. Results: The conventional guns functioned in fields of less than 7.5mT. Conversely, the redesigned diode required fields greater than .1T to function correctly. Magnetic shielding was feasible for SIDS of greater than 1000mm for field strengths of .5T and 1T, and 1100mm for 1.5 and 3.0T. Beyond these limits shielding resulted in unacceptable MRI distortion. In contrast, the redesigned diode could perform acceptably for SIDs of less than 812, 896, 931, and 974mm for imaging strengths of 0.5, 1.0, 1.5, 3.0T. Conclusions: For in-line MRIlinac configurations where the electron gun is operating in low field regions, shielding is a straight forward option. However, as magnetic field strength increases and the SID is reduced, shielding results in too great a distortion in the MRI and redesigning the electron optics is the preferable solution. The authors would like to acknowledge funding from the National Health and Research Council (AUS), National Institute of Health (NIH), and Cancer Institute NSW.

43 PARTICLE ACCELERATORS↗

TH-C-12A-08: New Compact 10 MV S-Band Linear Accelerator: 3D Finite-Element Design and Monte Carlo Dose Simulations

Purpose: To design a new compact S-band linac waveguide capable of producing a 10 MV x-ray beam, while maintaining the length (27.5 cm) of current 6 MV waveguides. This will allow higher x-ray energies to be used in our linac-MRI systems with the same footprint. Methods: Finite element software COMSOL Multiphysics was used to design an accelerator cavity matching one published in an experiment breakdown study, to ensure that our modeled cavities do not exceed the threshold electric fields published. This cavity was used as the basis for designing an accelerator waveguide, where each cavity of the full waveguide was tuned to resonate at 2.997 GHz by adjusting the cavity diameter. The RF field solution within the waveguide was calculated, and together with an electron-gun phase space generated using Opera3D/SCALA, were input into electron tracking software PARMELA to compute the electron phase space striking the x-ray target. This target phase space was then used in BEAM Monte Carlo simulations to generate percent depth doses curves for this new linac, which were then used to re-optimize the waveguide geometry. Results: The shunt impedance, Q-factor, and peak-to-mean electric field ratio were matched to those published for the breakdown study to within 0.1% error. After tuning the full waveguide, the peak surface fields are calculated to be 207 MV/m, 13% below the breakdown threshold, and a d-max depth of 2.42 cm, a D10/20 value of 1.59, compared to 2.45 cm and 1.59, respectively, for the simulated Varian 10 MV linac and brehmsstrahlung production efficiency 20% lower than a simulated Varian 10 MV linac. Conclusion: This work demonstrates the design of a functional 27.5 cm waveguide producing 10 MV photons with characteristics similar to a Varian 10 MV linac.

07 ISOTOPE AND RADIATION SOURCES↗

SU-E-J-111: Finite Element-Based Deformable Image Registration of Pleural Cavity for Photodynamic Therapy

Purpose: The pleural volumes will deform during surgery portion of the pleural photodynamic therapy (PDT) of lung cancer when the pleural cavity is opened. This impact the delivered dose when using highly conformal treatment techniques. In this study, a finite element-based (FEM) deformable image registration is used to quantify the anatomical variation between the contours for the pleural cavities obtained in the operating room and those determined from pre-surgery computed tomography (CT) scans. Methods: An infrared camera-based navigation system (NDI) is used during PDT to track the anatomical changes and contour the lung and chest cavity. A series of CTs of the lungs, in the same patient, are also acquired before the surgery. The structure contour of lung and the CTs are processed and contoured in Matlab and MeshLab. Then, the contours are imported into COMSOL Multiphysics 5.0, where the FEM-based deformable image registration is obtained using the deformed mesh - moving mesh (ALE) model. The NDI acquired lung contour is considered as the reference contour, and the CT contour is used as the target one, which will be deformed. Results: The reconstructed three-dimensional contours from both NDI and CT can be converted to COMSOL so that a three-dimensional ALE model can be developed. The contours can be registered using COMSOL ALE moving mesh model, which takes into account the deformation along x, y and z-axes. The deformed contour has good matches to the reference contour after the dynamic matching process. The resulting 3D deformation map can be used to obtain the locations of other critical anatomic structures, e.g., heart, during surgery. Conclusion: Deformable image registration can fuse images acquired by different modalities. It provides insights into the development of phenomenon and variation in normal anatomical structures over time. The initial assessments of three-dimensional registration show good agreement.

60 APPLIED LIFE SCIENCES↗

Polarity effects and apparent ion recombination in microionization chambers

Purpose: Microchambers demonstrate anomalous voltage-dependent polarity effects. Existing polarity and ion recombination correction factors do not account for these effects. As a result, many commercial microchamber models do not meet the specification of a reference-class ionization chamber as defined by the American Association of Physicists in Medicine. The purpose of this investigation is to determine the cause of these voltage-dependent polarity effects. Methods: A series of microchamber prototypes were produced to isolate the source of the voltage-dependent polarity effects. Parameters including ionization-chamber collecting-volume size, stem and cable irradiation, chamber assembly, contaminants, high-Z materials, and individual chamber components were investigated. Measurements were performed with electrodes coated with graphite to isolate electrode conductivity. Chamber response was measured as the potential bias of the guard electrode was altered with respect to the collecting electrode, through the integration of additional power supplies. Ionization chamber models were also simulated using COMSOL Multiphysics software to investigate the effect of a potential difference between electrodes on electric field lines and collecting volume definition. Results: Investigations with microchamber prototypes demonstrated that the significant source of the voltage-dependent polarity effects was a potential difference between the guard and collecting electrodes of the chambers. The voltage-dependent polarity effects for each prototype were primarily isolated to either the guard or collecting electrode. Polarity effects were reduced by coating the isolated electrode with a conductive layer of graphite. Polarity effects were increased by introducing a potential difference between the electrodes. COMSOL simulations further demonstrated that for a given potential difference between electrodes, the collecting volume of the chamber changed as the applied voltage was altered, producing voltage-dependent polarity effects in the chamber response. Ionization chamber measurements and COMSOL simulations demonstrated an inverse relationship between the chamber collecting volume size and the severity of voltage-dependent polarity effects on chamber response. The effect of a given potential difference on chamber polarity effects was roughly ten times greater for microchambers as compared to Farmer-type chambers. Stem and cable irradiations, chamber assembly, contaminants, and high-Z materials were not found to be a significant source of the voltage-dependent polarity effects. Conclusions: A potential difference between the guard and collecting electrodes was found to be the primary source of the voltage-dependent polarity effects demonstrated by microchambers. For a given potential difference between electrodes, the relative change in the collecting volume is smaller for larger-volume chambers, illustrating why these polarity effects are not seen in larger-volume chambers with similar guard and collecting electrode designs. Thus, for small-volume chambers, it is necessary to reduce the potential difference between the guard and collecting electrodes in order to reduce polarity effects for reference dosimetry measurements.

60 APPLIED LIFE SCIENCES↗

SU-F-I-50: Finite Element-Based Deformable Image Registration of Lung and Heart

Purpose: Photodynamic therapy (PDT) is used after surgical resection to treat the microscopic disease for malignant pleural mesothelioma and to increase survival rates. Although accurate light delivery is imperative to PDT efficacy, the deformation of the pleural volume during the surgery impacts the delivered light dose. To facilitate treatment planning, we use a finite-element-based (FEM) deformable image registration to quantify the anatomical variation of lung and heart volumes between CT pre-(or post-) surgery and surface contours obtained during PDT using an infrared camera-based navigation system (NDI). Methods: NDI is used during PDT to obtain the information of the cumulative light fluence on every cavity surface point that is being treated. A wand, comprised of a modified endotrachial tube filled with Intralipid and an optical fiber inside the tube, is used to deliver the light during PDT. The position of the treatment is tracked using an attachment with nine reflective passive markers that are seen by the NDI system. Then, the position points are plotted as three-dimensional volume of the pleural cavity using Matlab and Meshlab. A series of computed tomography (CT) scans of the lungs and heart, in the same patient, are also acquired before and after the surgery. The NDI and CT contours are imported into COMSOL Multiphysics, where the FEM-based deformable image registration is obtained. The NDI and CT contours acquired during and post-PDT are considered as the reference, and the Pre-PDT CT contours are used as the target, which will be deformed. Results: Anatomical variation of the lung and heart volumes, taken at different times from different imaging devices, was determined by using our model. The resulting three-dimensional deformation map along x, y and z-axes was obtained. Conclusion: Our model fuses images acquired by different modalities and provides insights into the variation in anatomical structures over time.

60 APPLIED LIFE SCIENCES↗

Volcanic arc rigidity variations illuminated by coseismic deformation of the 2011 Tohoku-oki M9

Rock strength has long been linked to lithospheric deformation and seismicity. However, independent constraints on the related elastic heterogeneity are missing, yet could provide key information for solid Earth dynamics. Using coseismic Global Navigation Satellite Systems (GNSS) data for the 2011 M9 Tohoku-oki earthquake in Japan, we apply an inverse method to infer elastic structure and fault slip simultaneously. We find compliant material beneath the volcanic arc and in the mantle wedge within the partial melt generation zone inferred to lie above ~100 km slab depth. We also identify low-rigidity material closer to the trench matching seismicity patterns, likely associated with accretionary wedge structure. Along with traditional seismic and electromagnetic methods, our approach opens up avenues for multiphysics inversions. Those have the potential to advance earthquake and volcano science, and in particular once expanded to InSAR type constraints, may lead to a better understanding of transient lithospheric deformation across scales.

58 GEOSCIENCES↗

Machine learning–aided real-time detection of keyhole pore generation in laser powder bed fusion

Porosity defects are currently a major factor that hinders the widespread adoption of laser-based metal additive manufacturing technologies. One common porosity occurs when an unstable vapor depression zone (keyhole) forms because of excess laser energy input. With simultaneous high-speed synchrotron x-ray imaging and thermal imaging, coupled with multiphysics simulations, we discovered two types of keyhole oscillation in laser powder bed fusion of Ti-6Al-4V. Amplifying this understanding with machine learning, we developed an approach for detecting the stochastic keyhole porosity generation events with submillisecond temporal resolution and near-perfect prediction rate. Finally, the highly accurate data labeling enabled by operando x-ray imaging allowed us to demonstrate a facile and practical way to adopt our approach in commercial systems.

42 ENGINEERING↗

A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media

Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly ill-conditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physics-based strategies. Current state-of-the-art “black-box” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics. We demonstrate the applicability of our framework when used as a “black-box” solver for multiphase poromechanics. Here, we show that the framework is flexible to accommodate a wide range of scenarios, as well as efficient and scalable for large problems.

97 MATHEMATICS AND COMPUTING↗

Landmark-Warped Emulators for Models with Misaligned Functional Response

Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.

97 MATHEMATICS AND COMPUTING↗

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding of their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multilayer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely, the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such a model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.

97 MATHEMATICS AND COMPUTING↗

Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality of the parameters and computational complexity of the PDE solves make such problems challenging. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to estimate the other parameters. In this article, hyper-differential sensitivity analysis (HDSA) is used to assess the sensitivity of the solution of the PDE-constrained optimization problem to changes in the auxiliary parameters. Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always practically feasible as a result of ill-posedness in the inverse problem. Here we introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates. Our proposed framework is demonstrated on a nonlinear multiphysics inverse problem motivated by estimation of spatially heterogeneous material properties in the presence of spatially distributed parametric modeling uncertainties.

97 MATHEMATICS AND COMPUTING↗