Accurate Multiobjective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization
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Abstract
The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. The multidimensional nature of the search necessitates exploration of multimillion compound libraries over which even density functional theory (DFT) screening is intractable. Machine learning (e.g., artificial neural network, ANN, or Gaussian process, GP) models for this task are limited by training data availability and predictive uncertainty quantification (UQ). We overcome such limitations by using efficient global optimization (EGO) with the multidimensional expected improvement (EI) criterion. EGO balances exploitation of a trained model with acquisition of new DFT data at the Pareto front, the region of chemical space that contains the optimal trade-off between multiple design criteria. We demonstrate this approach for the simultaneous optimization of redox potential and solubility in candidate M(II)/M(III) redox couples for redox flow batteries from a space of 2.8 M transition metal complexes designed for stability in practical redox flow battery (RFB) applications. We show that a multitask ANN with latent-distance-based UQ surpasses the generalization performance of a GP in this space. With this approach, ANN prediction and EI scoring of the full space are achieved in minutes. Starting from ca. 100 representative points, EGO improves both properties by over 3 standard deviations in only five generations. Analysis of lookahead errors confirms rapid ANN model improvement during the EGO process, achieving suitable accuracy for predictive design in the space of transition metal complexes. The ANN-driven EI approach achieves at least 500-fold acceleration over random search, identifying a Pareto-optimal design in around 5 weeks instead of 50 years.
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These techniques can be applied to the latent space of models just as readily as the feature space, for example, to highlight regions of promise for enrichment or to reveal governing design principles.
“These techniques can be applied to the latent space of models just as readily as the feature space, for example, to highlight regions of promise for enrichment (37,65) or to reveal governing design principles (64).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [37]
In Results and Discussion > Machine Learning Models (page unavailable), the paper uses distance in an ANN’s latent space to quantify uncertainty. In Results and Discussion > Design Outcomes (page unavailable), it uses expected improvement to select promising complexes for further calculation and model retraining. It does not explicitly identify promising regions in latent space for enrichment; the separate design-principles clause is cited to another source. (LLM, conf=0.82)
Experimental — accuracy not yet measuredJanet et al. used efficient global optimization with the 2D expected improvement criterion for multi-objective optimization of complexes with earth-abundant metals for redox flow battery applications, simultaneously improving predicted solubility in polar nonaqueous electrolytes and redox potential.
“Janet et al. (37) used EGO with the 2D expected improvement criterion for multi-objective optimization of complexes with earth-abundant metals (i.e., Cr, Mn, Fe, or Co) for redox flow battery applications.”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [37]
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredJanet et al. constructed a space of 2.8M homoleptic TMCs through combinatorial fusion and subsequent functionalization.
“Through combinatorial fusion and subsequent functionalization, Janet et al. (37) constructed a space of 2.8M homoleptic TMCs.”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [37]
In five generations, the best-performing materials all significantly exceeded those that could have been observed in diversity-oriented or random search-based screens, and properties were optimized at least 500-fold faster through the efficient global optimization algorithm.
“In five generations, the best-performing materials all significantly exceeded (37) those that could have been observed in diversity-oriented or random search-based screens (Figure 8).”
From Machine Learning for the Discovery, Design, and Engineering of Materials. (2022) · cites this paper as [37]
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AI Approaches to Homogeneous Catalysis with Transition Metal Complexes
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Why Conventional Design Rules for C–H Activation Fail for Open-Shell Transition-Metal Catalysts
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Self-citationUsing Machine Learning to Predict the Antibacterial Activity of Ruthenium Complexes**
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Directional multiobjective optimization of metal complexes at the billion-system scale
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AI-enabled materials discovery for advanced ceramic electrochemical cells
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Inverse Design of Pore Wall Chemistry To Control Solute Transport and Selectivity
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- Authors
- Janet, J. P., Ramesh, S., Duan, C., & Kulik, H. J.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Kulik, Heather J.
- Venue
- ACS Central Science
- Publisher
- American Chemical Society (ACS)
- Published
- 2020-03-11
- Volume
- 6
- Issue
- 4
- Pages
- 513-524
- ISSN
- 2374-7943 (ISSN-L)
- 2374-7951
- PMC
- PMC7181321
- OpenAlex
- W3012320417
- Cited by
- 200
- References
- 70
- Citations by year
- 2026: 14 · 2025: 23 · 2024: 25 · 2023: 41 · 2022: 37 · 2021: 41 · 2020: 18 · 2019: 1
- FWCI
- 13.33
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- Locations
- ACS Central Science (publishedVersion, other-oa)
- ChemRxiv (acceptedVersion, cc-by-nc-nd)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Royal College of Surgeons in Ireland (submittedVersion, cc-by-nc-nd)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- Funders
- Defense Advanced Research Projects Agency (D18AP00039)
- American Association for the Advancement of Science
- Basic Energy Sciences (DE-SC0018096)
- Office of Naval Research (N00014-18-1-2434)
- Burroughs Wellcome Fund
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced battery technologies research
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Multi-Objective Optimization Algorithms
- Keywords
- transition metal complexes, redox flow batteries, efficient global optimization, multi-objective design, Pareto front, redox potential, solubility, multi-task neural network, uncertainty quantification, chemical space exploration, machine learning screening
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