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DOE OSTI2026

Vanishing dynamic strength measured in a transient high-pressure phase of tin

This work reports two independent experimental estimations of the dynamic strength of the body-centered tetragonal (bct) 𝛾 phase of tin, which occurs at pressures above about 9 GPa and transforms promptly back to the ambient 𝛽 phase upon pressure release. Measuring strength in such a transient high-pressure phase is challenging. One measurement used free-surface Richtmyer-Meshkov instabilities generated with gas gun impact. Another set of measurements used ramp-release loading in a pulsed-power facility. Strength estimations came from comparison to simulations using a comprehensive multiphase modeling framework that includes equation of state, shear moduli, and strength separately for each phase, and treats mixed-phase regions. Both experimental methods found the 𝛾-phase strength to be very low, within experimental uncertainty of zero. The existing literature on other materials, by contrast, almost universally reports higher strength in transient high-pressure phases compared with ambient phases. Recent Molecular-Dynamics simulations on tin in the literature showed almost zero deviatoric strength during a deformation-induced bct → bct transformation in which one of the 𝛾-phase 𝑎 axes “flips” to the 𝑐 axis. This reorientation currently provides the most plausible explanation for the low observed strength in 𝛾-phase tin.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Systematic Validation of Ensemble Cloud-Process Simulations using Polarimetric Radar Observations and Simulator over the NASA Wallops Flight Facility

The BiLateral Operational Storm-Scale Observation and Modeling (BLOSSOM) project was initiated to establish a long-term supersite to improve understanding of cloud physical states and processes as well as to support satellite and climate model programs over the WFF site via a bilateral approach of storm-scale observations and process modeling. This study highlights a noble systematic validation framework of the BLOSSOM ensemble cloud-process simulations through mixed-phase, light-rain, and deep-convective precipitation cases. The framework consists of creating a domain-shifted ensemble of large-scale forcing datasets, and configuring and performing cloud-process simulations with three different bulk microphysics schemes. Validation uses NASA S-band dual-POLarimetric radar (NPOL) observations in the form of statistical composites and skill scores via a polarimetric radar simulator and newly developed CfRad Data tool (CfRAD). While the simulations capture the overall structures of the reflectivity composites, polarimetric signals are still poorly simulated, mainly due to a lack of representation of ice microphysics diversity in shapes, orientation distributions, and their complex mixtures. Despite the limitation, this new ensemble-based validation framework demonstrates that 1) no particular forcing or microphysics scheme outperforms the rest and 2) the skill scores of coarse- and fine-resolution ensemble simulations with different domain-shifted forcing and microphysics schemes are highly correlated with each other with no clear improvement. On the other hand, this suggests that coarse-resolution ensemble simulations are relevant for selecting the best meteorological forcing and microphysics scheme before conducting computationally demanding large eddy simulations (LESs) in support of aircraft and satellite instrument development as well as cloud-precipitation-convection parameterizations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

What can simulation test beds teach us about social science? Results of the ground truth program

The ground truth program used simulations as test beds for social science research methods. The simulations had known ground truth and were capable of producing large amounts of data. This allowed research teams to run experiments and ask questions of these simulations similar to social scientists studying real-world systems, and enabled robust evaluation of their causal inference, prediction, and prescription capabilities. We tested three hypotheses about research effectiveness using data from the ground truth program, specifically looking at the influence of complexity, causal understanding, and data collection on performance. We found some evidence that system complexity and causal understanding influenced research performance, but no evidence that data availability contributed. The ground truth program may be the first robust coupling of simulation test beds with an experimental framework capable of teasing out factors that determine the success of social science research.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Development of a Single-Phase, Transient, Subchannel Code, within the MOOSE Multi-Physics Computational Framework

Subchannel codes have been widely used for thermal-hydraulics analyses in nuclear reactors. This paper details the development of a novel subchannel code within the Idaho National Laboratory’s (INL) Multi-physics Object Oriented Simulation Environment (MOOSE). MOOSE is a parallel computational framework targeted at the solution of systems of coupled, nonlinear partial differential equations, that often arise in the simulation of nuclear processes. As such, it includes codes/modules able to solve the multiple linear and nonlinear physics that describe a nuclear reactor, under normal operation conditions or accidents. This includes thermal-hydraulics, fuel performance, and neutronics codes, between others. A MOOSE-based subchannel code is a new addition to the fleet of INL-developed codes, based on the MOOSE framework. In this work, we present the derivation of the subchannel equations for a single-phase fluid, we proceed with the description of the algorithm that is used to solve these equations and describe how this algorithm was implemented within MOOSE. We also present how this code can be coupled to the BISON fuel performance code. Next, we verify the friction model and the turbulent mixing model. We calibrate the turbulent modeling parameters for momentum mixing and enthalpy mixing, C T , β. We validate the code using experimental results and last demonstrate the coupling capabilities using a simple example.

42 ENGINEERING↗

DOE OSTI2024

New systems in MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) serves as a common library of classes between applications developed for advanced reactor analysis, fusion device engineering, spent fuel cask analysis, geochemistry studies, among other fields. These applications drive the development of the framework to meet their needs. Systems in MOOSE group capabilities that share a common purpose and generally common code. They can be leveraged by all downstream applications, providing extensive code re-use and shared maintenance. They facilitate the discovery by new users of the classes meeting at least partially their needs, and offer the same opportunities for customization as other systems. The addition of a new system to MOOSE opens new ways of solving or discretizing nonlinear problems, of performing distributed postprocessing, and a plethora of other needs. While new systems can be introduced in downstream applications rather than at the framework level, the framework team monitors common needs across the community and often triggers their addition. Documentation, training material, development needs can be centralized, limiting duplicated work across the community. The last three years have seen a large expansion in the capabilities of MOOSE. The supporting role of the framework in the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has created numerous feature requests to support neutronics, thermal hydraulics, computational fluid dynamics and thermo-mechanics simulations in the Griffin, SAM, Pronghorn and Bison applications respectively. Similarly, laboratory-directed research and development (LDRD) projects in additive manufacturing, high-Reynolds flow simulations, structure optimization also necessitate an expansion of the framework capabilities. This summary reports on the new systems created in MOOSE, their design, their capabilities and some of the relevant interfaces.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

A Physics-Informed Reinforcement Learning Framework for Economic-Thermal Co-Optimization of Crypto Mining Data Centers: Preprint

The rapid expansion of cryptocurrency mining has created a new class of high-density data centers characterized by extreme thermal flux and high sensitivity to volatile economic markets. Traditional thermal management strategies, typically reliant on rule-based control, maintain static setpoints that fail to account for fluctuating electricity prices and cryptocurrency values - factors critical to mining profitability. To address this, we present a physics-informed reinforcement learning (PIRL) framework for economic-thermal co-optimization in crypto mining data centers. This framework consists of a proximal policy optimization (PPO) agent, a virtual testbed powered by high-fidelity physics-based models, and an interactive frontend dashboard. The PPO agent is trained using the virtual testbed and strict hardware safety limits. This physics-informed approach allows the agent to learn a stochastic policy that dynamically balances mining revenue against operational costs by co-optimizing HVAC cooling setpoints and IT computational hashrate. The simulation results demonstrate that the integrated framework achieved an 8.62% increase in net operational profit compared to traditional baseline strategies while strictly adhering to safety-critical temperature constraints (coolant supply temperature < 32 degrees C). This work provides a scalable template for the deployment of reinforcement learning in mission critical facilities where economic volatility and physical safety must be managed simultaneously.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

A Moving Embedded Boundary Approach for the Compressible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1], [91], [92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds - acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries - an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re = 40, an inline oscillating cylinder at Re = 100, and a transversely oscillating cylinder at Re = 185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

adaptive refinement↗

DOE OSTI2024

Analyzing the Effects of Atmospheric Turbulent Fluctuations on the Wake Structure of Wind Turbines and Their Blade Vibrational Dynamics

In recent trends, a rising demand for renewable energy has driven wind turbines to larger proportions, where lighter blade designs are often adopted to reduce the costs associated with logistics and production. This causes modern utility-scale wind turbine blades to be inherently more flexible, and their amplified aeroelastic sensitivity results in complex multi-physics reactions to variant atmospheric conditions, including dynamic patterns of aerodynamic loading at the rotor and vortex structure evolutions within the wake. In this paper, we analyze the influence of inflow variance for wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex wake interactions for a range of flexible NRT blade variations, operating in differing conditions of variant atmospheric flow. CODEF solutions of turbine operation in Steady-In-The-Average (SITA) wind conditions are compared to SITA wind conditions featuring a controlled gust-like pulse overimposed, to isolate the effects of typical wind fluctuations. Finally, simulations of realistic time-varying wind conditions from SWiFT meteorological tower measurements are compared to the solutions of SITA wind conditions. These increasingly complex atmospheric inflow variations are tested to show the differing effects evoked by various patterns of spatiotemporal atmospheric flow fluctuations. An analysis is presented for solutions of wind turbine aeroelastic response and vortex wake evolution, to elucidate the consequences of variant inflow, which pertain to wind turbine dynamics at an individual and farm-collective scale. The comparisons of simulated farm flow for SITA and measured fluctuating wind conditions show that certain regions of the wake contain up to a 12% difference in normalized axial velocity, due to the introduction of wind fluctuations. The findings of this study prove valuable for practical applications in wind farm control and optimization strategies, with particular significance for modern utility-scale wind power plants operating in variant atmospheric conditions.

Farrell, Alayna (ORCID:000000023555720X)↗

DOE OSTI2025

Modeling and Analysis of Wind Turbine Wake Vortex Evolution Due to Time-Constant Spatial Variations in Atmospheric Flow

Modern utility-scale wind turbines are evolving toward larger, lighter, and more flexible designs to meet the growing demand for renewable energy while minimizing logistical costs. However, these advancements in lightweight design result in heightened aeroelastic sensitivity, leading to complex interactions which affect the rotor’s capacity to withstand aerodynamic loading and the cascading effects that manifest in the wake’s vortex-structure evolution under variable atmospheric conditions. In this paper, we analyze the influence of stream-wise fluctuating atmospheric flow conditions on wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex–wake interactions for a range of conditions with spatially variant atmospheric flow. CODEF solutions for turbine operation in wind conditions featuring only one parameter fluctuation are compared to wind conditions with several wind parameter variations in combination. By isolating individual inflow variations and comparing them to multi-parameter scenarios, we determine the contributions of each atmospheric factor to rotor dynamics, wake evolution, and downstream wind farm interactions. The purpose of this paper is to analyze the effects of spatial variations in atmospheric flow on the topological evolution of wind turbine vortex wakes, which constitutes a gap in the current understanding of wind turbine wake dynamics. The insights gained from this study are particularly valuable for the development of wind farm control strategies aimed at mitigating the adverse effects of wake interactions, enhancing energy capture, and improving the overall stability of wind farm operations. With these insights, we aim to contribute to the development of modeling and simulation tools to optimize utility-scale wind power plants operating in diverse atmospheric environments.

Farrell, Alayna (ORCID:000000023555720X)↗

DOE OSTI2023

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Real-time Simulation of Coordinated Sub-Transmission Volt-Var Control Tool under High Distributed PV Penetration

With the rapid penetration of intermittent solar photovoltaic (PV) and other distributed energy resources (DER) into the grid, and subsequent changes in power flow patterns in both distribution and sub-transmission, voltage regulation is becoming a major challenge. It is prudent to leverage PV and DER to provide ancillary services to the grid, such as voltage regulation. Recently, a quasi-static, coordinated real-time sub transmission volt-var control algorithm (CReST-VCT) was developed for voltage regulation under high PV penetration by dispatching the reactive power settings of the shunt devices and PV inverters. The algorithm was validated offline, on a quasistatic study. Such quasi-static dispatching algorithms cannot guarantee its performance for highly nonlinear dynamical power systems. In this paper the performance of the algorithm is validated with a real time nonlinear dynamic simulation of a modified IEEE 118 bus system in Opal-RT. The real time simulation is used to emulate the actual system operation, providing a more realistic testing environment for CReST-VCT. The dispatch and control signals are communicated between the power system (Opal solver) and the control center (GAMS solver) in real-time with a MODBUS bridge. The results demonstrate i) system is stable with the new dispatch points ii) significant improvement in system-wide voltage profiles compared to an uncontrolled scenario. Another significant contribution of the work is developing a framework for dispatchable, long duration dynamic simulations that can be leveraged for market/dispatch studies.

CReST-VCT, Opal-RT, Volt/Var Control, renewable in↗

DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 1: inline modeling of polarized cross beam energy transfer and subsequent drive anomalies on OMEGA and NIF

Inertial confinement fusion experiments are sensitive to cross-beam energy transfer (CBET), a laser-plasma instability that redistributes laser energy in the coronal plasma through self-generated ion acoustic wave (IAW) gratings. The detailed CBET coupling depends on the polarization state of the crossing wavefields. CBET itself can also scramble the beam polarizations by inducing ellipticity through the IAW grating, and rotating the seed polarization toward that of the pump. We develop a ray-based model that describes the polarized CBET coupling and that is compatible with the framework of 3D inline radiative hydrodynamics simulations. The model is implemented in the ASTER/IFRIIT code and verified against an academic test case and an offline polarized CBET post-processor. It is then applied to the detailed configuration of the distributed polarization rotator system on OMEGA, where results highlight how polarized CBET induces significant low modes in the collisional absorption source term. Finally, the modeling is applied to a simple indirect-drive configuration, comparing CBET calculations with 96 unpolarized or polarized beams with 24 unpolarized quads. It is shown that these cases produce similar power amplification per cone of beams grouped with similar polar angles. However, the 96 beam geometry itself is found to reduce azimuthal variations in quad power after the interaction and favors beams with larger polar angles within the cones, an effect that is amplified by the polarized CBET. Application of the model to inline calculations of OMEGA implosions are presented in a companion paper.

3D inline modeling↗

DOE OSTI2022

High Performance Adaptive Physics Refinement to Enable Large-Scale Tracking of Cancer Cell Trajectory

The ability to track simulated cancer cells through the circulatory system, important for developing a mechanistic understanding of metastatic spread, pushes the limits of today's supercomputers by requiring the simulation of large fluid volumes at cellular-scale resolution. To overcome this challenge, we introduce a new adaptive physics refinement (APR) method that captures cellular-scale interaction across large domains and leverages a hybrid CPU-GPU approach to maximize performance. Through algorithmic advances that integrate multi-physics and multi-resolution models, we establish a finely resolved window with explicitly modeled cells coupled to a coarsely resolved bulk fluid domain. In this work we present multiple validations of the APR framework by comparing against fully resolved fluid-structure interaction methods and employ techniques, such as latency hiding and maximizing memory bandwidth, to effectively utilize heterogeneous node architectures. Collectively, these computational developments and performance optimizations provide a robust and scalable framework to enable system-level simulations of cancer cell transport.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

A Poromechanical Framework for Internal Interactions Induced by Solid Inclusions

The framework of poromechanics is generalized to simulate the multiscale behavior of porous media subjected to internal loadings stemming from the growth of solid inclusions. This generalization is designed to enable the study of anisotropic internal stress generation from solid growth within the pores, while recovering isotropic fluid-induced loading as a particular case. For this purpose, a mathematical strategy to define constitutive tensors in a thermodynamically consistent form is proposed, thus offering new opportunities for determining the poromechanical properties of a porous solid through advanced experimentation or micromechanical models. The framework is specialized by means of established elastic solutions for single pore–matrix interaction, as well as through homogenization schemes considering the interaction among congruent pores. In particular, the second Eshelby solution and the Tanaka–Mori–Benveniste homogenization scheme are used to derive a microporoelastic model. At an elemental scale, the model is tested under mixed control conditions by replicating different scenarios of geomaterial testing. In addition, the model characteristics are outlined with reference to inelastic microscopic loadings replicating chemo-mechanical forcing, such as expansive crystal formation. Through a series of parametric analyses, it is shown that the microstructure of the pores significantly influences the properties of porous media. Most notably, it is shown that the effects of a solid forming within the pores depend in a highly nonlinear fashion on the constitutive characteristics of the inhomogeneities and can therefore not be readily quantified or predicted without models capturing the diverse multiscale interactions among pores, inhomogeneities, and matrix.

chemomechanics↗

DOE OSTI2025

Model-free estimation of completeness, uncertainties, and outliers in atomistic machine learning using information theory

Abstract An accurate description of information is relevant for a range of problems in atomistic machine learning (ML), such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Modeling Offshore Wind Farm Performance in Coastal Low-Level Jets Using Coupled Mesoscale-Microscale Large Eddy Simulations

Accurately predicting wind farm reliability under complex offshore atmospheric conditions remains a key challenge, particularly during noncanonical meteorological events such as coastal low-level jets (LLJs). LLJs, characterized by strong nonmonotonic vertical shear and directional veer, depart significantly from the simplified inflow assumptions embedded in conventional design standards, low-fidelity engineering models, and microscale large eddy simulations of the atmospheric boundary layer. In this work, we use the virtual wind farm framework—an exascale, graphics processing unit–accelerated large eddy simulation platform coupled with high-fidelity aeroservoelastic turbine models and advanced mesoscale-microscale coupling via the ExaWind software stack—to investigate turbine responses under realistic LLJ forcing. Simulations are performed over the U.S. North Atlantic offshore domain with the use of meteorological inputs from New York State Energy Research and Development Authority buoy data, focusing on a representative LLJ case impacting the International Energy Agency 15 MW reference turbine. Our results show that LLJs can cause up to 50% power deficits in downstream turbine rows and significantly amplify low-speed shaft and tower loads through nonlinear coupling between complex inflow characteristics and turbine structural dynamics. Two primary mechanisms drive these load amplifications: (1) unique LLJ inflow features—including veer and vertical/lateral shear—and (2) the downstream evolution of the flow under stable thermal stratification, which suppresses turbulence mixing and alters wake recovery. These mechanisms produce streamwise variations in turbine loading not captured by standard hub height–based metrics or existing design load case (DLC) definitions. This study highlights the critical role of rotor-scale flow gradients in driving fatigue and system-level aeroelastic responses, challenging current DLC and control strategies. We advocate the integration of full-flow field, environment-aware wind inputs into load modeling and control algorithms. By leveraging exascale computing to resolve mesoscale-microscale coupling, this work lays the groundwork for next-generation offshore wind turbine design and operation in meteorologically complex marine environments.

17 WIND ENERGY↗

DOE OSTI2026

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of cAhemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.

42 ENGINEERING↗