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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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DOE OSTI2023

Joint Optimization for Transport and Bucket Loading Phases of Automated Wheel Loaders

This article investigates optimization of fuel-efficiency and productivity for automated wheel loaders. A control-oriented model for both the transport phase and bucket loading phase is proposed. Here, the vehicle model includes an automatic gear shift schedule that can be incorporated into the optimization problem. Based on the model, the multistage optimization problem is formulated to simultaneously consider all phases of a short cycle with physical constraints. Cycle time and fuel efficiency are used as the weighted performance indexes in a multiobjective cost function. Bucket fill factor is included as a constraint during the bucket loading phase. A nonlinear programming problem is created with collocation using MATLAB and CasADi. The optimization solver IPOPT solves the problem to obtain the optimal state and control trajectories, which can be used as a reference for automated wheel loaders or even as a driver advisory for human-driven wheel loaders.

42 ENGINEERING↗

DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

A Two-Stage Quantum Reinforcement Learning Method for Multi-Objective Transmission Switching

Multi-objective transmission switching (MO-TS) problems involve the strategic reconfiguration of network topology to simultaneously optimize multiple objectives. As the system scale increases, finding feasible solutions becomes increasingly challenging due to the problem's nonlinearity and high computational complexity. To address these challenges, this paper proposes a two-stage quantum reinforcement learning method that leverages potential quantum advantages for MO-TS. In the first stage, candidate switching lines are identified using a graph-theoretical approach to reduce the problem's dimensionality. The second stage introduces a quantum-classical reinforcement learning framework, where a learnable measurement-based CNN-ResVQC architecture is developed to effectively reduce the input dimension for quantum processing, mitigate vanishing gradients, and enhance trainability while improving the quantum circuit's flexibility in modeling complex decision policies for MO-TS. Numerical studies on IEEE 14-bus, 57-bus, and 118-bus systems demonstrate that the proposed algorithm achieves superior training stability and faster convergence with approximately 1% of the network parameters required by classical algorithms, highlighting its effectiveness, efficiency, and scalability. Furthermore, the practicality is validated through its stable convergence under three common quantum noise channels.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2026

Searching for the Most Harmful Field Errors in the HSR IR Superconducting Magnets

In this project, we improve beam stability for the Electron-Ion Collider. Magnetic field errors can reduce beam stability, making it essential to identify the field errors that have the greatest impact on accelerator performance. However, this is particularly challenging because beam stability depends on the complex interactions of many magnetic field errors, resulting in a high-dimensional and nonlinear optimization problem. We determine which field errors are the most influential for the large physical aperture superconducting magnet B2PF, a critical magnet in the Interaction Region (IR) in the Hadron Storage Ring (HSR). We complete and analyze nearly 30,000 simulations on the Brookhaven National Laboratory Linux Cluster by varying 18 nonlinear magnetic field errors. We evaluate beam stability using the dynamic aperture and the tune diffusion. We identify the field errors that most strongly influence beam stability and establish quantitative field error tolerances that improve accelerator performance.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Frequency Recovery in Power Grids Using High-Performance Computing

Maintaining electric power system stability is paramount, especially in extreme contingencies involving unexpected outages of multiple generators or transmission lines that are typical during severe weather events. Such outages often lead to large supply-demand mismatches followed by subsequent system frequency deviations from their nominal value. The extent of frequency deviations is an important metric of system resilience, and its timely mitigation is a central goal of power system operation and control. This paper develops a novel nonlinear model predictive control (NMPC) method to minimize frequency deviations when the grid is affected by an unforeseen loss of multiple components. Our method is based on a novel multi-period alternating current optimal power flow (ACOPF) formulation that accurately models both nonlinear electric power flow physics and the primary and secondary frequency response of generator control mechanisms. We develop a distributed parallel Julia package for solving the large-scale nonlinear optimization problems that result from our NMPC method and thereby address realistic test instances on existing high-performance computing architectures. Our method demonstrates superior performance in terms of frequency recovery over existing industry practices, where generator levels are set based on the solution of single-period classical ACOPF models.

nonlinear model predictive control↗

DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗

DOE OSTI2021

DART-PFLOTRAN: An ensemble-based data assimilation system for estimating subsurface flow and transport model parameters

Ensemble-based Data Assimilation (EDA), based on the Monte Carlo approach, has been effectively applied to estimate model parameters through inverse modeling in subsurface flow and transport problems. However, implementation of EDA approach involves a complicated workflow that include setting up and executing ensemble forward model simulations, processing observations and model simulation results for parameter updates, and repeat for sequential or iterative EDA. To facilitate the management of such workflow and lower the barriers for adopting EDA-based parameter estimation in subsurface science, we develop a generic software frame-work linking the Data Assimilation Research Testbed (DART) with a massively parallel subsurface FLOw and TRANsport code PFLOTRAN. The new DART-PFLOTRAN leverages both the core data assimilation engines in DART and the computational power afforded by PFLOTRAN. In addition to the standard smoother and filtering options, DART-PFLOTRAN enables an iterative EDA workflow based on the Ensemble Smoother for Multiple Data Assimilation method (ES-MDA) to improve estimation accuracy for nonlinear forward problems. Here, we verify the implementation of ES-MDA in DART-PFLOTRAN using two synthetic cases designed to estimate static permeability and dynamic exchange fluxes across the riverbed, respectively, from continuous temperature measurements made across a depth profile. One-dimensional hydro-thermal simulations are performed in both cases to relate temperature responses with the parameters of interest. In the case of estimating dynamic parameters, we demonstrate the flexibility of DART-PFLOTRAN in automating sequential ES-MDA workflow, which will significantly reduce the time researchers spend on managing complex workflows in similar applications. Both studies yield accurate estimations of the parameters compared to their synthetic truth, while ES-MDA leads to more accurate estimation when a high level of nonlinearity exist between observed responses and unknown parameters. With a code base in Python and Fortran, DART-PFLOTRAN paves the way for applications in large-scale subsurface inverse modeling by automating the complex workflow of sequential ES-MDA that can be executed on various computing platforms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Nonlinear, real-time optimization for actuator management in tokamaks

Experiments in DIII-D have been carried out to test a novel actuator management approach in tokamaks. Here, the actuator management scheme is posed as a nonlinear-optimization problem in which the actuator commands are calculated in real time according to the changing control priorities, plasma state, and actuator availability. Such optimization problem is solved using the augmented Lagrangian method, combined with a gradient projection method and a conjugate-gradient iteration algorithm. The algorithmic approach followed in this work does not depend on the particular control objectives or actuators considered, which facilitates its integration with other independently-designed control components within a plasma-control system. In addition, the actuator-management algorithm is able to handle the optimization problem in a computationally efficient manner, making it suitable for real-time implementations. Initial DIII-D results in the steady-state high-q min scenario have demonstrated the capabilities of the actuator manager to perform both simultaneous multiple mission and repurposing sharing, which will be required in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Integrated control of individual plasma scalars with simultaneous neoclassical tearing-mode suppression

A novel integrated-control architecture has been tested in nonlinear, one-dimensional simulations using the control-oriented transport simulator (COTSIM©) and in DIII-D experiments. Integrated architectures that can perform continuous-mission control while also handling off-normal events will be vital in future reactor-grade tokamaks. Continuous-mission controllers for individual magnetic and kinetic scalars (thermal stored-energy (W), volume-average toroidal rotation (Ω Φ ), and safety factor profile (q) at different spatial locations) have been integrated in this work with event-triggered neoclassical tearing-mode (NTM) suppression controllers by combining them into an architecture augmented by a supervisory and exception handling (S&EH) system and an actuator management (AM) system. Here, the AM system, which enables the integration of competing controllers, solves in real time a nonlinear optimization problem that takes into account the high-level control priorities dictated by the S&EH system. The resulting architecture offers a high level of integration and some of the functionalities that will be required to fulfill the advanced-control requirements anticipated for ITER. Initial simulations using COTSIM suggest that the plasma performance and its MHD stability may be improved under integrated feedback control. In addition, the integrated-control architecture has been implemented in the DIII-D plasma control system and tested experimentally for the first time ever in DIII-D in a high-q min scenario, which is a candidate for steady-state operation in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

DOE OSTI2022

Modeling approaches for addressing unrelaxable bound constraints with unconstrained optimization methods

We explore novel approaches for solving nonlinear optimization problems with unrelaxable bound constraints, which must be satisfied before the objective function can be evaluated. Our method reformulates the unrelaxable bound-constrained problem as an unconstrained optimization problem that is amenable to existing unconstrained optimization methods. The reformulation relies on a domain warping to form a merit function; the choice of the warping determines the level of exactness with which the unconstrained problem can be used to find solutions to the bound-constrained problem, as well as key properties of the unconstrained formulation such as smoothness. We develop theory when the domain warping is a multioutput sigmoidal warping, and we explore the practical elements of applying unconstrained optimization methods to the formulation. Here, we develop an algorithm that exploits the structure of the sigmoidal warping to guarantee that unconstrained optimization algorithms applied to the merit function will find a stationary point to the desired tolerance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Microstructural changes and mass transport in cement-based materials: A modeling approach

Highlights: • Concept to relate microstructural changes, mass transport, and chemical reactions in cement-based materials is presented. • Multi-physics modeling approach utilizing an extended version of the PNP equation and the geochemical code IPHREEQC. • Case studies indicate significant changes in mass transport properties due to alterations in the microstructure. • Microstructural changes depend on exposure and interactions between chemical reactions, pore structure, and mass transport. A generic modeling framework is presented to relate microstructural changes, i.e. changes in the pore volume distribution and phase assemblage, and mass transport in cement-based materials. The modeling framework accounts for mass transport and chemical equilibrium between ions in the pore solution and solid hydrates by means of an extended version of the Poisson-Nernst-Planck equation, in which the chemical equilibrium is solved by the external geochemical code IPHREEQC. Results of numerical studies concerning carbonation and leaching of a cement-based material indicate significant changes in mass transport properties due to chemical reactions leading to alterations in the microstructure. The resulting highly non-linear (both spatial and temporal) microstructural changes are thereby depending on the exposure and indicate that interactions between chemical reactions, pore structure changes, and mass transport have to be accounted for as a whole.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Joint inversion of electromagnetic measurements for the determination of water saturation profiles in concrete structures

Highlights: • DC-electrical and dielectric data are combined to estimate concrete saturation degree. • A joint inversion approach of the electromagnetic measurements is proposed. • The sensitivity of the measurements to the saturation model parameters is analysed. • The new joint approach was developed and is applied to synthetic and real data. • The benefits of the joint approach over the inversion of one data type are highlighted. Water saturation profiles in concrete are essential to assess its durability and can be determined using non-destructive techniques, especially the electric and the capacitive methods. In this paper, we propose a new inversion scheme where both resistivity and permittivity measurements are inverted jointly to retrieve the saturation profile. The finite element method is used to model the measurements in 3D, the concrete having a saturation profile with depth, represented by a continuous model taking the form of a Weibull curve with four parameters. A non-linear least-squares optimization based on the Levenberg-Marquardt scheme is developed for the inversion of measurements. Results show that information gathered from both measurements enriches the reconstructed profile, leading to a more reliable estimation of saturation profiles. We believe that the joint inversion method herein developed could lead to the study of more complex phenomena, such as the coupled water-chloride ingress.

36 MATERIALS SCIENCE↗