Compositionally complex and High Entropy Alloys via physics-informed  artificial intelligence

We are, by any reasonable estimate, still at the very beginning of materials discovery. Of the roughly 10⁸⁰ chemically meaningful multi-element combinations that we could in principle synthesize, we use on the order of 10⁴ materials industrially today. We see this gap as the central motivation for pushing beyond binary and ternary alloy design into compositionally complex systems — high-entropy alloys, multi-principal-element ceramics, chemically graded superalloy microstructures, and near-atomic-scale-blended semiconductor stacks. When we add elements to a solid solution, we do far more than shift a point on a phase diagram: we perturb the electronic density of states, introduce or suppress magnetic ordering, break local crystal symmetry, generate short-range order, and — this is the part we find most consequential for engineering properties — we change the formation energies, migration barriers and binding behavior of point defects, dislocations and interfaces, often exponentially with composition. Because materials are essentially never used in thermodynamic equilibrium but in metastable, defect-populated states, we cannot separate the question of chemical complexity from the question of microstructural complexity: one drives the other.

We rely on density functional theory (DFT) as our most rigorous quantum-mechanical tool for extracting energetics, but we are constrained by supercell sizes that are far too small to sample the configurational space of a five- or six-component random solid solution with proper statistical representation of local chemical environments. We do not expect quantum computing to resolve this bottleneck for large, chemically complex systems in the near term. When we move to molecular dynamics with machine-learning-trained interatomic potentials, we can reach larger system sizes and include kinetics, but we still depend on how faithfully the potential reproduces the true multi-body energy landscape. At the mesoscale, we use phase-field and crystal-plasticity frameworks to couple chemistry, elasticity and diffusion, but these methods rely on coarse-grained Landau-type free-energy approximations whose fidelity is only as good as the underlying thermodynamic description.
We find a particularly instructive failure mode in the Cantor-type FeMnCrNiCo family. This alloy combines some of the strongest ferromagnetic (Fe, Co, Ni) and antiferromagnetic (Mn, Cr) elements within a single metastable solid solution, so we must simultaneously capture the correct magnetic ground states across all relevant spin configurations and properly account for configurational, vibrational, magnetic and electronic entropy contributions — not just the configurational term that dominates simple mixing models. Most empirical potentials do not have the functional flexibility to do this, and as a result even well-established bottom-up atomistic approaches fail to reproduce known experimental phase boundaries in these systems. We see an analogous, and at first counterintuitive, phenomenon in high-entropy ceramics: despite their strong covalent/ionic bonding and localized electrons — a chemistry we would traditionally expect to be enthalpy-dominated — disorder-induced charge fluctuations and configurational entropy on the anion sublattice open up mixing behavior and compositional space that we would not predict from classical ionic-bonding arguments alone.
Given these constraints, we often fall back on physics-based descriptors: computationally tractable quantities with high leverage on the properties we care about. A recurring example in our own and related work is the use of DFT-computed stacking-fault energy as a proxy for phase stability, deformation-twinning propensity and martensitic transformability in high-entropy alloys. We couple such descriptors to crystal-plasticity or phase-field solvers to predict mechanical response, and this strategy has enabled us to design alloys such as metastable dual-phase high-entropy systems in which two coexisting phases undergo complementary, load-triggered transformation-induced plasticity and twinning-induced plasticity mechanisms. What we cannot yet do with descriptor-based approaches is resolve the full energetic-kinetic-microstructure-property chain in a single, generalizable framework — each descriptor is tied to the specific mechanism we identified as rate-limiting for that particular problem.

 Accelerating the design of compositionally complex materials via physics-informed artificial intelligence

• We use an iterative active-learning loop — coupling machine learning, AI-guided experiments and DFT-based phase-equilibrium calculations — to identify new FeNiCo-based Invar compositions (alloys with near-zero thermal expansion), closing the loop between thermodynamic simulation and targeted experimental validation rather than screening blindly.
• We apply symbolic regression, guided by sure-independence-screening and sparsifying-operator approaches, to derive closed-form analytical expressions linking lattice constant and cohesive energy to the bulk modulus of perovskites — recovering physically interpretable descriptors rather than an opaque regression surface.
• We use random-forest models trained against DFT-computed entropy-forming-ability metrics to screen multi-component disordered metal carbides, from which we flagged around 70 new candidate high-entropy ceramic compositions for further validation.
• We have shown, in the case of nickel-base superalloys, that a neural network trained on experimental and CALPHAD-derived thermodynamic data can optimize compositions across strength, corrosion resistance and phase stability simultaneously — a multi-objective, high-dimensional design problem that we consider essentially intractable for forward physics models alone, given the coupling between processing history, γ/γ′ microstructure and mechanical/oxidation response