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DOE OSTI2022

Multi-objective goal-directed optimization of de novo stable organic radicals for aqueous redox flow batteries

Abstract Advances in the field of goal-directed molecular optimization offer the promise of finding feasible candidates for even the most challenging molecular design applications. One example of a fundamental design challenge is the search for novel stable radical scaffolds for an aqueous redox flow battery that simultaneously satisfy redox requirements at the anode and cathode, as relatively few stable organic radicals are known to exist. To meet this challenge, we develop a new open-source molecular optimization framework based on AlphaZero coupled with a fast, machine-learning-derived surrogate objective trained with nearly 100,000 quantum chemistry simulations. The objective function comprises two graph neural networks: one that predicts adiabatic oxidation and reduction potentials and a second that predicts electron density and local three-dimensional environment, previously shown to be correlated with radical persistence and stability. With no hard-coded knowledge of organic chemistry, the reinforcement learning agent finds molecule candidates that satisfy a precise combination of redox, stability and synthesizability requirements defined at the quantum chemistry level, many of which have reasonable predicted retrosynthetic pathways. The optimized molecules show that alternative stable radical scaffolds may offer a unique profile of stability and redox potentials to enable low-cost symmetric aqueous redox flow batteries.

25 ENERGY STORAGE↗

NASA NTRS1992

Conditions for continuation of the efficient curve for multi-objective control-structure optimization

The paper describes the conditions for continuation of the efficient curve for bi-objective control-structure optimization of a ten-bar truss with two collocated sensors and actuators. The curve has been obtained with an active set algorithm using a homotopy method. The curve is discontinuous. A general stability theory has been implemented to determine sufficient conditions for the persistence of minima, and bifurcation theory has been used to characterize the possible points of discontinuity of the path.

Rakowska, Joanna↗

NASA NTRS1992

Tracing the efficient curve for multi-objective control-structure optimization

A recently developed active set algorithm for tracing parameterized optima is adapted to multiobjective optimization. The algorithm traces a path of Kuhn-Tucker points using homotopy curve tracking techniques, and is based on identifying and maintaining the set of active constraints. Second order necessary optimality conditions are used to determine nonoptimal stationary points on the path. In the bi-objective optimization case the algorithm is used to trace the curve of efficient solution (Pareto optima). As an example, the algorithm is applied to the simultaneous minimization of the weight and control force of a ten-bar truss with two collocated sensors and actuators, with some interesting results.

Rakowska, J.↗

DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Modeling the CEBAF Injector at 200 kV: Investigating K-Long Beam Conditions with and without Wien Filter

The upcoming K-Long experiment [1] ain Hall D at Jefferson Lab presents unique beam requirements, featuring a significantly low bunch repetition rate and an unusually high bunch charge. This experiment, which utilizes the CEBAF accelerator in conjunction with the GlueX experimental setup, aims to study strange hadron spectroscopy by measuring the differential cross section and polarizations of produced hyperons such as Λ, Σ, Ξ, and Ω. By directing an intense K-Long beam towards the LD2/LH2 target, new and valuable data can be obtained. To optimize the CEBAF injector specifically for this experiment, we employed Multi-Objective Genetic Optimization (MGO) using General Particle Tracer (GPT) simulations. Through this approach, we determined the optimal magnetic elements and radiofrequency (RF) settings required to achieve a K-Long bunch charge of 0.64 pC at an energy of 200 kV. We conducted simulations with both the Wien Filter turned on and off to examine its impact on the beam. Furthermore, we investigated the transmission efficiency and beam characteristics of electron beams with varying charge per bunch through the injector, considering the simultaneous operation of all four CEBAF Halls. The results of our study offer valuable insights and guidance for optimizing the CEBAF injector not only for the Jefferson Lab K-Long experiment but also for other experiments that entail similar beam conditions.

Pokharel, Sunil↗

DOE OSTI2023

Modeling for the phased injector upgrade for 12 GeV CEBAF

The upcoming Jefferson Lab K-Long experiment at Hall D will require unique beam conditions with a much lower bunch repetition rate and atypically high bunch charge. To optimize the Continuous Electron Beam Accelerator Facility (CEBAF) injector for this experiment, we performed Multi-Objective Genetic Optimization (MGO) using General Particle Tracer (GPT) to determine the magnetic elements and RF settings necessary for the K-long bunch charge (0.64 pC) at 200 kV. We also investigated the transmission and beam characteristics of low to high charge per bunch electron beams through the injector for simultaneous operations of all four CEBAF Halls and characterized the transmission as a function of the photocathode laser spot size and pulse length. Our findings provide valuable insights into optimizing the CEBAF injector for the Jefferson Lab K-Long experiment, as well as for other experiments with similar beam conditions

Kazimi, R.↗

DOE OSTI2024

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗

DOE OSTI2020

Conjugate Heat Transfer Analysis of the Supercritical CO2 Based Counter Flow Compact 3D Heat Exchangers

Compact heat exchangers using supercritical fluids such as CO2 are preferred due to their high heat transfer capacity and smaller footprint. Three-dimensional conjugate forced convection heat transfer analysis was performed on several shell-and-tube counter-flow microchannel heat exchangers. Numerical simulations were conducted to test effect of change in mass flow rate, hydraulic diameter and various cross sections on the heat transfer. Increasing mass flow rate improved heat transfer up to a maximum value and then decreased downstream with increasing turbulence. Maximum heat transfer was obtained for the micro channel with the smallest hydraulic diameter. Amongst the cross sections analyzed (circular, square, circular with radial ribs, and square with radial ribs), the most uniform distribution of temperature and maximum heat transfer were obtained for circular cross section with radial ribs. An optimally efficient operation of such a heat exchanger can be attained by considering these factors during multi-objective constrained optimization of geometric parameters and requirements for additive manufacturing of such compact heat exchangers.

Chitale, Janhavi↗

NASA NTRS1997

CONDUIT: A New Multidisciplinary Integration Environment for Flight Control Development

A state-of-the-art computational facility for aircraft flight control design, evaluation, and integration called CONDUIT (Control Designer's Unified Interface) has been developed. This paper describes the CONDUIT tool and case study applications to complex rotary- and fixed-wing fly-by-wire flight control problems. Control system analysis and design optimization methods are presented, including definition of design specifications and system models within CONDUIT, and the multi-objective function optimization (CONSOL-OPTCAD) used to tune the selected design parameters. Design examples are based on flight test programs for which extensive data are available for validation. CONDUIT is used to analyze baseline control laws against pertinent military handling qualities and control system specifications. In both case studies, CONDUIT successfully exploits trade-offs between forward loop and feedback dynamics to significantly improve the expected handling, qualities and minimize the required actuator authority. The CONDUIT system provides a new environment for integrated control system analysis and design, and has potential for significantly reducing the time and cost of control system flight test optimization.

Tischler, Mark B.↗

DOE OSTI2020

Conjugate Heat Transfer Analysis of the Supercritical CO2 Based Counter Flow Compact 3D Heat Exchangers

Chitale, Janhavi↗

NASA NTRSDate not supplied

Exploring Transfers Between Earth-Moon Halo Orbits via Multi-Objective Reinforcement Learning

Multi-Reward Proximal Policy Optimization, a multi-objective deep reinforcement learning algorithm, is used to examine the design space of low-thrust trajectories for a SmallSat transferring between two libration point orbits in the Earth-Moon system. Using Multi-Reward Proximal Policy Optimization, multiple policies are simultaneously and efficiently trained on three distinct trajectory design scenarios. Each policy is trained to create a unique control scheme based on the trajectory design scenario and assigned reward function: a unique combination of weights scaling competing objectives that guide the spacecraft to the target mission orbit, incentivize faster flight times, and penalize propellant mass usage. Then, the policies are evaluated on the same set of perturbed initial conditions in each scenario to generate the propellant mass usages, flight times, and state discontinuities from a reference trajectory for each control scheme. This solution space of low-thrust trajectories for a SmallSat is used to examine the multi-objective trade space for the trajectory design scenario. By autonomously constructing the solution space, insights into the required propellant mass, flight time, and transfer geometry are rapidly achieved.

Christopher J Sullivan↗

DOE OSTI2024

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

CALPHAD-based Bayesian optimization to accelerate alloy discovery for high-temperature applications

Two crucial properties influencing the performance of high-temperature alloys are coefficient of thermal expansion (CTE) and phase constitution. It is desirable to have alloys with low CTE, which reduces CTE mismatch with the surface oxide and the likelihood of oxide spallation. Reducing the amount of brittle intermetallic phases such as Sigma (σ) enhances alloy ductility and processability. Here, we propose a multi-objective Bayesian Optimization (BO) model to simultaneously minimize CTE (at an operational temperature of 1150 °C) and T σ (temperature when the Sigma phase completely dissolves in the metal matrix), properties which are obtained from high-throughput CALculation of PHAse Diagrams (CALPHAD). The model successfully identifies several alloys with CTE ≤ 2 × 10 –5 /K and T σ ≤ 500 °C by exploring just 7% of the nickel–chromium–cobalt–aluminum–iron (Ni–Cr–Co–Al–Fe) composition space. Such multi-objective alloy design frameworks can be used to inform additive manufacturing experiments and accelerate alloy discovery for high-temperature energy applications.

36 MATERIALS SCIENCE↗

NASA NTRS2005

Development and Testing of Control Laws for the Active Aeroelastic Wing Program

The Active Aeroelastic Wing research program was a joint program between the U.S. Air Force Research Laboratory and NASA established to investigate the characteristics of an aeroelastic wing and the technique of using wing twist for roll control. The flight test program employed the use of an F/A-18 aircraft modified by reducing the wing torsional stiffness and adding a custom research flight control system. The research flight control system was optimized to maximize roll rate using only wing surfaces to twist the wing while simultaneously maintaining design load limits, stability margins, and handling qualities. NASA Dryden Flight Research Center developed control laws using the software design tool called CONDUIT, which employs a multi-objective function optimization to tune selected control system design parameters. Modifications were made to the Active Aeroelastic Wing implementation in this new software design tool to incorporate the NASA Dryden Flight Research Center nonlinear F/A-18 simulation for time history analysis. This paper describes the design process, including how the control law requirements were incorporated into constraints for the optimization of this specific software design tool. Predicted performance is also compared to results from flight.

Dibley, Ryan P.↗

DOE OSTI2026

Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization

We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.

Mulkin, Olivier↗

DOE OSTI2022

AI-Enabled Discovery and Physics-Based Optimization of Energy Efficient Processing Strategies for Advanced Turbine Alloys (Final Technical Report)

In this project, the multi-organizational team of academic and industrial researchers from the University of Kentucky an aerospace and energy generation OEM partner has leveraged novel Digital Process Twin (DPT) models of process/structure interactions (i.e., process-induced surface integrity) to advance a paradigm of fully integrated computational materials engineering (ICME). Using efficient process models as the core of a digital process simulator for a reinforcement learning algorithm, the team has integrated industrial data and metrics of structure/performance/energy relationships and manufacturing-related energy metrics to optimize dynamic processing parameters for significantly improved life-cycle energy efficiency of advanced γ-TiAl low-pressure turbine (LPT) alloys, as indicated by a set of design relevant parameters (e.g., residual stresses and scrap rate). The key objective and anticipated outcome of the project was at least a 10% reduction in life-cycle embodied energy for a recently developed, γ-TiAl low-pressure turbine (LPT) alloy and nickel-based superalloy Inconel 718, through the adoption of the proposed AI-enabled process optimization approach. The final project outcomes significantly exceeded this original target, realizing manufacturing-related energy efficiency improvements of more than 130% for TiAl and up to 80% for Inconel 718. Rather than following the prevailing and highly inefficient empirical paradigm, the proposed study demonstrated the feasibility of adopting a digital, physics-based process design and optimization paradigm. The recurring need for manual intervention, rework, reinspection causes significant production bottlenecks and unnecessary expense associated with delivering the requisite component quality. The OEM partner, and turbine industry in general, expect to reap significant cost and resource savings if an AI-optimized set of parameters can be applied to specific machining operations. The technical scope of the proposed project involved the paving of a realistic path towards model-based and AI-enabled Integrated Computational Materials Engineering (ICME), and away from inefficient empirical process optimization and legacy manufacturing practices, which are no longer able to efficiently process novel high-performance turbine alloy materials. The project team will address the fundamental knowledge gap that currently exists within the ICME paradigm with respect to the process/structure/performance/energy impacts of finishing processes. While significant resources have been devoted to the ‘early stages’ of manufacturing, such as alloy design, primary and secondary processing, finishing processes have not been adequately integrated within ICME. To provide an actionable path towards model-based finishing process design (e.g., machining, burnishing, grinding, polishing), we will employ a novel AI-enabled process optimization paradigm, based on a computationally efficient, physics-based process simulator. Through limited experimental work to calibrate and validate our process simulator model via an advanced in-situ characterization technique and process optimization via reinforcement learning, the project will seek to demonstrate a viable alternative to the inefficient ‘legacy’ processing strategies, empirical testing and broad scope machining learning approaches, all of which fail to adequately consider complex process physics. The project team has identified an intermetallic γ-TiAl LPT alloy, which is currently being used as part of the OEM partner’s advanced gas turbine designs. This particular alloy poses significant manufacturing challenges during finishing operations, which limit the degree to which the current turbine design can be manufactured in an energy- and cost-efficient manner. Empirical testing and numerical modeling efforts to optimize processing parameters for γ-TiAl have not been able to resolve these manufacturing challenges, so the proposed physics-based AI-enabled optimization technology would offer a truly novel and transformative capability. The multi-organizational team of academic and industry experts from the UKY and the OEM partner will work together closely to demonstrate the analytical and experimental critical function and characteristic proof of concept of this novel approach.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2023

Techno-economic life cycle assessment of CO 2 -EOR operations towards net negative emissions at farnsworth field unit

Optimizations of CO 2 Water Alternating Gas(WAG)- systems with multi-objectives of incremental recovery and maximization of CO 2 storage are challenging. Here, the incorporation of a total Greenhouse gas (GHG) life cycle assessment is mostly ignored leading to inaccurate estimation of overall net carbon emissions of their operations. In this study, the effect of a total GHG life cycle assessment on a multi-objective CO 2 -WAG optimization with integrated techno-economic assessment (TEA) which factors carbon tax credit is conducted. A life cycle assessment (LCA) was conducted utilizing a 20 -year optimized post history matched data from a high fidelity reservoir simulation model. Using data generated from the optimum result, a techno-economic life cycle analysis was further conducted. The first scenario classified as the base model had an estimated 81% of purchased CO 2 sequestered. The results through a comprehensive techno-economic LCA model yielded a net estimate of 73% of purchased CO 2 . The optimized forecasted model which considered key operational and reservoir factors such as WAG ratio, injection rates and periods, and well specification resulted in an improved sequestration of 92% of purchased CO 2 . However, this also dropped to 84% after taking it through LCA. These results clearly indicate a significant amount of net CO 2 is not accounted for when operations are not analyzed through LCA. From the LCA, direct flaring volumes of CO 2 , energy consumption and efficiency of unit equipment were noticed to be the major causes of these reductions. Considering ten main sources of energy as source of energy generation, a comparative techno-eco LCA was conducted. The results confirmed a lower net volume and NPV for energy sources with higher carbon footprints and vice versa. Thus, a total LCA of CO 2 -WAG greatly influences net storage factor of purchased CO 2 and hence project NPV where tax credit/incentives per ton of CO 2 sequestered is considered. Although operational conditions are optimized for best results, there are significant factors that leads to minimization of net storage factor. This study therefore provides an insightful information for optimizing CO 2 -WAG multi-objectives to achieve minimum GHG emission.

02 PETROLEUM↗

DOE OSTI2020

Featureless adaptive optimization accelerates functional electronic materials design

Electronic materials that exhibit phase transitions between metastable states (e.g., metal-insulator transition materials with abrupt electrical resistivity transformations) are challenging to decode. For these materials, conventional machine learning methods display limited predictive capability due to data scarcity and the absence of features that impede model training. In this article, we demonstrate a discovery strategy based on multi-objective Bayesian optimization to directly circumvent these bottlenecks by utilizing latent variable Gaussian processes combined with high-fidelity electronic structure calculations for validation in the chalcogenide lacunar spinel family. We directly and simultaneously learn phase stability and bandgap tunability from chemical composition alone to efficiently discover all superior compositions on the design Pareto front. Previously unidentified electronic transitions also emerge from our featureless adaptive optimization engine. Our methodology readily generalizes to optimization of multiple properties, enabling co-design of complex multifunctional materials, especially where prior data is sparse.

36 MATERIALS SCIENCE↗