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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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Final Report DE-FE0031785 Mohsen Ahmadian, Ph.D. Demonstration of Proof of Concept of a Multiphysics Approach for Real-Time Remote Monitoring of Dynamic Changes in Pressure and Salinity in Hydraulically Fractured Networks

Hydraulic fracturing has evolved into a multistep process with varying flow rates, carrier fluids (e.g., gel or slickwater), proppant loadings, and proppant grain sizes. As a result, primary recovery from a hydraulically fractured tight-oil reservoir is often a tiny fraction of the original oil in place, ranging between 5 and 10%. As stated in the FOA1990, “part of this problem is due to the inability of current well completion processes to effectively stimulate the entire reservoir volume in contact with the wellbore. Innovative technologies are needed that can help improve the effectiveness of reservoir completion methods, maximize stimulated reservoir volumes, and optimize recovery over the entire producing life span of a well”. We first need to enhance the current fracture diagnostic techniques to improve a well-completion design. However, detecting and delineating a subsurface hydraulic fracture is extremely difficult because the induced fracture network is only fractionally propped, and these propped fractures are generally very thin. Microseismic and tiltmeter monitoring techniques can provide information on the fracture extent but provide little or no information on the movement and final distribution of proppant or production fluids. On the other hand, electromagnetic (EM) imaging has shown the capability to monitor proppant distribution throughout the fracture area, especially in the presence of Electrically Active Proppants (EAPs). A previous EM survey of hydraulic fracturing at the Devine Fracture Pilot Site (DFPS) and subsequent EM code developments demonstrated this survey as a robust technique to remotely interrogate the extent of the EAP-filled hydraulic fracture during its propagation. The objectives of the project were threefold: (1) to capitalize on the material properties of an EAP to demonstrate remote monitoring of relative changes in pressure, pressure, and flow that are commonly encountered during production from a hydraulically fractured reservoir; (2) to evaluate EM imaging tools, to achieve Objective 1 in near real-time; and (3) to develop a multi-physics joint inversion approach to precisely predict flow patterns and physiochemical changes within an EAP-filled fracture network. This research project was built upon our previous work at the Devine Test Site managed by the Bureau of Economic Geology (BEG) at The University of Texas at Austin (UT-Austin). It also leveraged a significant investment from the Advanced Energy Consortium (AEC) to address the DOE's interest in subsurface flow, containment, and characterization by multiple signals. This three-year and three-month project succeeded in demonstrating the feasibility of a real-time dynamic fluid flow mapping technique at Technology Readiness Level 5 (TRL5) by utilizing a commercially available surface-based Controlled-Source Electromagnetic (CSEM) method (Objectives 1, 2). We demonstrated that injections into an EAP-filled fracture could be successfully coupled with real-time electric field measurements on the surface, leading to remote monitoring of dynamic changes within the EAP-filled fracture. Furthermore, the observed electric field in our study is influenced by bottomhole pressure, flow rate, and salinity, which is demonstrated by comparing these parameters with the electrical field potentials. EM simulations solely based on assumptions of fracture conductivity changes during injection did not reproduce the whole measured electric field magnitudes. Preliminary estimates showed that including Streaming Potential (SP) in our geophysical model is likely needed to reduce the simulation misfit.

02 PETROLEUM↗
DOE OSTI2021

Friction of Metals: A Review of Microstructural Evolution and Nanoscale Phenomena in Shearing Contacts

The friction behavior of metals is directly linked to the mechanisms that accommodate deformation. We examine the links between mechanisms of strengthening, deformation, and the wide range of friction behaviors that are exhibited by shearing metal interfaces. Specifically, the focus is on understanding the shear strength of nanocrystalline and nanostructured metals, and conditions that lead to low friction coefficients. Grain boundary sliding and the breakdown of Hall–Petch strengthening at the shearing interface are found to generally and predictably explain the low friction of these materials. While the following is meant to serve as a general discussion of the strength of metals in the context of tribological applications, one important conclusion is that tribological research methods also provide opportunities for probing the fundamental properties and deformation mechanisms of metals.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Electrical Resistivity Changes During Heating Experiments Unravel Heterogeneous Thermal‐Hydrological‐Mechanical Processes in Salt Formations

Abstract Rock salt is considered a suitable medium for the permanent disposal of heat‐generating radioactive waste due to its isolation properties. However, excavation damage and heating induce complex and heterogeneous thermal‐hydrological‐mechanical (THM) processes across different zones. Quantifying this heterogeneity is crucial for accurate long‐term performance assessment models, but traditional methods lack the necessary resolution. This study employs 4D electrical resistivity tomography (ERT) monitoring during controlled heating experiments in a salt formation to unravel the spatiotemporal dynamics of THM processes. Advanced time‐lapse inversion and clustering analysis quantify subsurface properties and map the heterogeneity of THM dynamics. The ERT results can estimate subsurface properties and delineate the damaged and intact zones, enabling appropriate parameterization and representation of processes for long‐term modeling. This approach may be used in further improving the predictive models and ensuring the safe long‐term disposal of radioactive waste in rock salt.

58 GEOSCIENCES↗
DOE OSTI2023

A smart alarm for particle accelerator beamline operations

We present the initial results of a proof-of-concept 'smart alarm' for the Continuous Electron Beam Accelerator Facility injector beamline at Jefferson Lab. To minimize machine downtime and improve operational efficiency, an autonomous alarm system able to identify and diagnose unusual machine states is needed. Our approach leverages a trained neural network capable of alerting operators (a) when an anomalous condition exists in the beamline and (b) identifying the element setting that is the root cause. The tool is based on an inverse model that maps beamline readings (diagnostic readbacks) to settings (beamline attributes operators can modify). The model takes as input readings from the machine and computes machine settings which are compared to control setpoints. Instances where predictions differ from setpoints by a user-defined threshold are flagged as anomalous. Given data corresponding to 354 anomalous injector configurations, the model can narrow the root cause of an anomalous condition to three potential candidates with 94.6% accuracy. Furthermore, compared to the current method of identifying anomalous conditions which raises an alarm when machine parameters drift outside their normal tolerances, the data-driven model can identify 83% more anomalous conditions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Brittle failure analysis and modeling of high-burnup PWR fuel cladding alloys

The aim of this research is the development of methods for predicting mechanical behavior and identification of limiting conditions to prevent brittle failure of high-burnup (HBU) pressure water reactor (PWR) fuel cladding alloys. A finite element (FE) model of the ring compression test (RCT) was created to analyze the failure behavior of zirconium-based alloys with radial hydrides during the RCT. An elastic-plastic material model describes the zirconium alloy. The stress-strain curve needed for the elastic-plastic material model was derived by inverse finite element analyses. Cohesive zone modeling is used to reproduce sudden load drops during RCT loading. Based on the failure mechanism in non-irradiated ZIRLO (R) claddings, a micro-mechanical model was developed that distinguishes between brittle failure along hydrides and ductile failure of the zirconium matrix. Two different cohesive laws representing these types of failure are present in the same cohesive interface. The key differences between these constitutive laws are the cohesive strength, the stress at which damage initiates, and the cohesive energy, which is the damage energy dissipated by the cohesive zone. Statistically generated matrix-hydride distributions were mapped onto the cohesive elements and simulations with focus on the first load drop were performed. Computational results are in good agreement with the RCT results conducted on high-burnup M5 (R) samples. It could be shown that crack initiation and propagation strongly depend on the specific configuration of hydrides and matrix material in the fracture area.

Simbruner, Kai↗
DOE OSTI2023

Field evaluation of semi‐automated moisture estimation from geophysics using machine learning

Geophysical methods can provide three-dimensional (3D), spatially continuous estimates of soil moisture. However, point-to-point comparisons of geophysical properties to measure soil moisture data are frequently unsatisfactory, resulting in geophysics being used for qualitative purposes only. This is because (1) geophysics requires models that relate geophysical signals to soil moisture, (2) geophysical methods have potential uncertainties resulting from smoothing and artifacts introduced from processing and inversion, and (3) results from multiple geophysical methods are not easily combined within a single soil moisture estimation framework. To investigate these potential limitations, an irrigation experiment was performed wherein soil moisture was monitored through time, and several surface geophysical datasets indirectly sensitive to soil moisture were collected before and after irrigation: ground penetrating radar, electrical resistivity tomography (ERT), and frequency domain electromagnetics (FDEM). Data were exported in both raw and processed form, and then snapped to a common 3D grid to facilitate moisture prediction by standard calibration techniques, multivariate regression, and machine learning. A combination of inverted ERT data, raw FDEM, and inverted FDEM data was most informative for predicting soil moisture using a random regression forest model (one-thousand 60/40 training/test cross-validation folds produced root mean squared errors ranging from 0.025–0.046 cm 3 /cm 3 ). This cross-validated model was further supported by a separate evaluation using a test set from a physically separate portion of the study area. Machine learning was conducive to a semi-automated model-selection process that could be used for other sites and datasets to locally improve accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗
DOE OSTI2026

Thermal property characterization of phase change materials in building applications: A systematic review of fundamentals, recent progress, and future directions

Phase change materials (PCMs) can reduce building peak loads and enable demand-responsive thermal energy storage (TES), but their deployment depends on reliable measurement and interpretation of thermal properties across laboratory, intermediate, and application scales. Here, this review systematically examines characterization methods, testing protocols, and recent advances for neat PCMs and PCM composites, emphasizing thermal conductivity, enthalpy-related properties (phase change temperature, latent heat, specific heat), and cycling stability. For thermal conductivity, we compare steady-state and transient techniques and note limitations when phase transition and contact resistance affect measurements. For enthalpy–temperature characterization, we discuss differential scanning calorimetry together with intermediate- and bulk-scale methods, including T-history, heat flow meter testing, and three-layer calorimetry (3LC), to generate application-relevant enthalpy–temperature profiles. Cycling stability is organized into four experimental families: thermoelectric–air, fully thermoelectric, water-bath, and in situ chamber approaches, with attention to separating reversible supercooling from true degradation such as phase segregation. We highlight emerging noncontact diagnostics, including infrared thermography and embedded sensing, for spatially resolved validation and multiscale interpretation. Finally, we review the growing use of AI and machine learning for property prediction, inverse characterization from experimental signals, and real-time state estimation in building-integrated TES. Key needs include harmonized protocols, interlaboratory benchmarking, uncertainty reporting, and metadata-rich datasets to accelerate reproducible PCM qualification for grid-flexible buildings.

AI↗
DOE OSTI2023

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. Furthermore, this workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

42 ENGINEERING↗
DOE OSTI2024

Palladium at high pressure and high temperature: A combined experimental and theoretical study

Palladium is one of the most important technological materials, yet its phase diagram remains poorly understood. At ambient conditions, its solid phase is face-centered cubic (fcc). However, another solid phase of Pd, body-centered cubic (bcc), was very recently predicted in two independent theoretical studies to occur at high pressures and temperatures. In this work, we report an experimental study on the room-temperature equation of state (EOS) of Pd to a pressure of 80 GPa, as well as a theoretical study on the phase diagram of Pd including both fcc-Pd and bcc-Pd. Our theoretical approach consists in ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase transition boundaries. We obtain the melting curves of both fcc-Pd and bcc-Pd and an equation for the fcc–bcc solid–solid phase transition boundary as well as the thermal EOS of Pd which is in agreement with experimental data and QMD simulations. We uncover the presence of another solid phase of Pd on its phase diagram, namely, random hexagonal close-packed (rhcp), and estimate the location of the rhcp-bcc solid–solid phase transition boundary and the rhcp–fcc–bcc triple point. We also discuss the topological similarity of the phase diagrams of palladium and silver, the neighbor of Pd in the periodic table. We argue that Pd is a reliable standard for shock-compression studies and present the analytic model of its principal Hugoniot in a wide pressure range.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Enhanced resonant ultrasound spectroscopy for measurement of the elastic properties of multi-material systems

Understanding the elastic properties of materials is critical for their safe incorporation and predictable performance. Current methods of bulk elastic characterization often have notable limitations for in situ structural applications, with usage restricted to simple geometries and material distributions. To address these existing issues, this study sought to expand the capabilities of resonant ultrasound spectroscopy (RUS), an established nondestructive evaluation method, to include the characterization of isotropic multi-material samples. In this work, finite-element-based RUS analysis consisted of numerical simulations and experimental testing of composite samples comprised of material pairs with varying elasticity and density contrasts. Utilizing genetic algorithm inversion and mode matching, our results demonstrate that elastic properties of multi-material samples can be reliably identified within several percent of known or nominal values using a minimum number of identified resonance modes, given sample mass is held consistent. The accurate recovery of material properties for composite samples of varying material similarity and geometry expands the pool of viable samples for RUS and advances the method towards in situ inspection and evaluation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Palladium at high pressure and high temperature: A combined experimental and theoretical study

Palladium is one of the most important technological materials, yet its phase diagram remains poorly understood. At ambient conditions, its solid phase is face-centered cubic (fcc). However, another solid phase of Pd, body-centered cubic (bcc), was very recently predicted in two independent theoretical studies to occur at high pressures and temperatures. In this work, we report an experimental study on the room-temperature equation of state (EOS) of Pd to a pressure of 80 GPa, as well as a theoretical study on the phase diagram of Pd including both fcc-Pd and bcc-Pd. Our theoretical approach consists in ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase transition boundaries. We obtain the melting curves of both fcc-Pd and bcc-Pd and an equation for the fcc–bcc solid– solid phase transition boundary as well as the thermal EOS of Pd which is in agreement with experimental data and QMD simulations. We uncover the presence of another solid phase of Pd on its phase diagram, namely, random hexagonal close-packed (rhcp), and estimate the location of the rhcp-bcc solid–solid phase transition boundary and the rhcp–fcc–bcc triple point. We also discuss the topological similarity of the phase diagrams of palladium and silver, the neighbor of Pd in the periodic table. We argue that Pd is a reliable standard for shock-compression studies and present the analytic model of its principal Hugoniot in a wide pressure range.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Sensitivity of a Subject-specific Ankle Sprain Simulation to Extrinsic Versus Intrinsic Biomechanical Factors

Ankle sprains are the most common musculoskeletal injury in sport and military activity, despite existing prophylactic strategies. The purpose of this report was to develop a probabilistic simulation of lateral ankle sprains during single-limb drop landing, towards accelerating innovation in ankle sprain prevention. A deterministic, subject-specific musculoskeletal model was extended with automation and probabilistic distributions on sprain-related biomechanical factors. Probabilistic simulations were generated using traditional Monte Carlo techniques and the advanced mean value method, a more computationally-efficient approach. Predicted distributions of peak ankle joint rotations, velocities, and moments borne by supporting passive structures agreed favorably with the deterministic model and with reports of real sprain biomechanics. Parameter sensitivities identified that predictions were most strongly influenced by drop height, subtalar joint posture at contact, invertor/evertor co-activation, and passive ankle stiffness. The advanced mean value method predicted confidence bounds comparable to a 1000-trial Monte Carlo simulation, and required only 14 model evaluations and 4-min processing time. The extended probabilistic simulation may be useful to virtually test new prophylactic strategies for ankle sprains, and is made available for open-source use (https://simtk.org/projects/sprain-sim).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Deep learning workflow for the inverse design of molecules with specific optoelectronic properties

The inverse design of novel molecules with a desirable optoelectronic property requires consideration of the vast chemical spaces associated with varying chemical composition and molecular size. First principles-based property predictions have become increasingly helpful for assisting the selection of promising candidate chemical species for subsequent experimental validation. However, a brute-force computational screening of the entire chemical space is decidedly impossible. To alleviate the computational burden and accelerate rational molecular design, we here present an iterative deep learning workflow that combines (i) the density-functional tight-binding method for dynamic generation of property training data, (ii) a graph convolutional neural network surrogate model for rapid and reliable predictions of chemical and physical properties, and (iii) a masked language model. As proof of principle, we employ our workflow in the iterative generation of novel molecules with a target energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Applying Bayesian inference and deterministic anisotropy to retrieve the molecular structure ∣Ψ(R)∣2 distribution from gas-phase diffraction experiments

Abstract Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. Here we address this inverse problem by developing a broadly applicable method that approximates the molecular frame structure ∣Ψ( R , t )∣ 2 distribution independent of these complex simulations. We retrieve the vibronic ground state ∣Ψ( R )∣ 2 for both simulated stretched NO 2 and measured N 2 O. From measured N 2 O, we observe 40 mÅ coordinate-space resolution from 3.75 Å −1 reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO 2 diffraction experiments, typical to high signal-to-noise levels predict 100–1000X resolution improvements, down to 0.1 mÅ. By directly measuring the width of ∣Ψ( R )∣ 2 , we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Antineutrino energy spectrum unfolding based on the Daya Bay measurement and its applications

The prediction of reactor antineutrino spectra will play a crucial role as reactor experiments enter the precision era. The positron energy spectrum of 3.5 million antineutrino inverse beta decay reactions observed by the Daya Bay experiment, in combination with the fission rates of fissile isotopes in the reactor, is used to extract the positron energy spectra resulting from the fission of specific isotopes. This information can be used to produce a precise, data-based prediction of the antineutrino energy spectrum in other reactor antineutrino experiments with different fission fractions than Daya Bay. The positron energy spectra are unfolded to obtain the antineutrino energy spectra by removing the contribution from detector response with the Wiener-SVD unfolding method. Consistent results are obtained with other unfolding methods. A technique to construct a data-based prediction of the reactor antineutrino energy spectrum is proposed and investigated. Given the reactor fission fractions, the technique can predict the energy spectrum to a 2% precision. In addition, we illustrate how to perform a rigorous comparison between the unfolded antineutrino spectrum and a theoretical model prediction that avoids the input model bias of the unfolding method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Denoising diffusion probabilistic models for generative alloy design

Inverse material design is an extremely challenging optimization task made difficult by, in part, the highly nonlinear relationship linking performance with composition. Quantitative approaches have improved significantly owing to advances in high throughput experimentation and computational thermodynamics. However, existing physics-based tools are mostly forward models; input a chemistry and obtain a prediction. More recently the materials community has leveraged advances in the machine learning community to establish novel inverse design frameworks. Very recently denoising diffusion probabilistic models have been shown to be extremely powerful generators producing synthetic data of various modalities e.g. images, text, audio, tables, etc.. In this work a novel framework for alloy design and optimization is proposed leveraging these class of models. Five key generative tasks are demonstrated (1) unconditional generation (2) composition conditioned generation (3) property conditioned generation (4) multi-feedstock conditioned generation and (5) generative optimization. These methods were tested on three case studies: high entropy alloy design, superalloy binder jet additive manufacturing, and in-situ dual-feedstock wire-arc additive manufacturing. Results indicate that the established models are extremely flexible, expressive, and robust. The architecture’s flexibility and training procedure empower the model to learn complex intra-compositional and composition-property relationships. Furthermore, the probabilistic nature of these models makes them well suited for addressing solution non-uniqueness and tackling uncertainty quantification tasks. While the fidelity and quantity of the underlying training data is paramount, we envision that future alloy design frameworks will make extensive use of these kinds of machine learning models as “search” tools bolstering the utility of experimental and computational approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands

Abstract The accurate modeling of water and heat transport in soils is crucial for both geo-environmental and geothermal engineering. Traditional modeling methods are problematic because they require well-defined boundaries and initial conditions. Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. In this study, we applied PINNs to tackle hydraulic and thermal transport coupling forward problems in silty sands. A fully connected deep neural network was utilized for training. This neural network model leverages automatic differentiation to apply the governing equations as constraints, based on the mathematical approximations established by the neural network itself. We conducted forward problems and compared the solutions derived from PINNs with those from Finite Element Method (FEM) simulations. The forward problem results demonstrate the PINNs model’s capability in predicting hydraulic transport, heat transport, and thermal–hydraulic coupling in silty sands under various boundary conditions. The PINNs exhibited great performance in simulating the thermal–hydraulic coupling problem. The accuracy of the PINNs solutions shows its potential for simulation in geotechnical engineering.

Feng, Yuan↗