Physics informed inverse discovery of potential topological materials via descriptor-graph ensemble learning

Quantum Topological Data Encoding

Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce \emph{quantum topological data encoding} (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.

MANDALA: An E(3)-Equivariant Graph Neural Network Framework for Learning Electronic-Structure Operators with Observable Guidance

Mandala is a modular software framework for learning block-sparse electronic-structure matrices with E(3)-equivariant graph neural networks that connects electronic-structure learning and observable-guided modeling while retaining a representation tied to quantum-mechanical operators rather than only scalar or vector targets as in MLIPs.

UniPocket: Physics-Aware Geometric Graph Learning with Manifold Completeness for Ligand-Specific Binding Site Prediction

UniHam: A Large-Scale SOC-Complete Dataset and Benchmark for Hamiltonian Learning in Materials

Accurate prediction of electronic Hamiltonians would enable broad property inference while avoiding the high computational cost of Density Functional Theory (DFT). However, progress toward general-purpose materials foundation models is limited by a data bottleneck: existing Hamiltonian datasets are typically small, lack structural diversity, and often omit essential relativistic physics such as spin--orbit coupling (SOC). We therefore construct UniHam, a large-scale Hamiltonian dataset and benchmark suite comprising 100,000+ DFT-computed complex-valued Hermitian Hamiltonians with full SOC, covering 72 elements and a wide range of crystal geometries and symmetries (spanning diverse lattice types and space-group families). Building on UniHam, we benchmark two representative state-of-the-art models under a standardized protocol and introduce complementary evaluation metrics that jointly assess three dimensions: (i) Hamiltonian reconstruction accuracy, (ii) out-of-distribution (OOD) generalization across composition/symmetry shifts, and (iii) the ability to support downstream property prediction from the predicted Hamiltonians. Experiments on UniHam demonstrate that the proposed benchmark and metrics effectively differentiate model capabilities, revealing intrinsic SOC- and element-dependent failure modes, large variations in compositional OOD robustness, and the necessity of spectral-level evaluation to assess whether Hamiltonian predictions reliably support downstream electronic-structure properties. Overall, UniHam provides a reproducible, SOC-complete benchmark that can sharpen model comparisons and accelerate the development of next-generation foundation models for quantum materials.

SAGE-Net: Semantics-Augmented Geometric Encoder for Material Property Prediction

Reliable structure-property modeling is crucial for accelerating materials discovery, where crystal graphs and structure-derived crystallographic descriptions provide complementary geometric and semantic information. Existing multimodal materials models primarily incorporate textual information through post-encoding fusion, latent-space alignment, or attention-based representation interaction mechanisms. However, in most cases, crystallographic semantics are introduced after structural encoding and therefore cannot directly guide the formation of atom-level crystal-graph representations. Here, we present Semantics-Augmented Geometric Encoder Network (SAGE-Net), a flexible multimodal framework that injects description-derived chemical and crystallographic semantics into geometric message passing. SAGE-Net introduces Semantic-Guided Message Passing (SGMP), which gates atom-level updates and enables crystallographic semantics to directly modulate local geometric interactions across multiple graph neural network (GNN) backbones. Across benchmarks covering bandgap, mechanical, transport-related properties, and synthesizability assessment, the SAGE-Net instantiated with different GNN backbones achieves the lowest MAE on eight out of ten JARVIS-DFT regression targets and delivers strong or highly competitive performance against both structure-based and multimodal baselines. For synthesizability assessment, the SAGE-Net demonstrate outstanding classification performance and high recall rates. Interpretability analysis unravels that SAGE-Net effectively captures physically interpretable crystallographic features, viz. space group, dimensionality, polyhedral environments, among others. Together, these results demonstrate SGMP-based SAGE-Net as a general and transferable framework for deeply integrated multimodal materials learning.

Machine Learning Materials Properties by Encoding Orbital-Projected Density of States

Graph neural networks have become the dominant machine-learning architecture for predicting materials properties from crystal structures. Yet the initialization of atomic node features has received comparatively little attention, and conventional approaches rely on static elemental descriptors that carry no information about the quantum-mechanical electronic environment of each atom in its crystalline host. Here we show that augmenting atomic node representations with site-projected orbital density of states (pDOS) fingerprints, computed directly from density functional theory calculations, yields systematic and substantial improvements in predictive performance.These representations are fused with Pettifor elemental embeddings at each atomic site before message passing. For the superconducting critical temperature $T_c$ and the optical dielectric constant $\epsilon_{\infty}$,the pDOS augmentation reduces prediction errors by 22.9% and 27.9%, respectively, relative to the elemental-descriptor baseline. These improvements are comparable to those achieved by doubling the training-set size. The gains are, however, contingent on training-set size. For the magnetic exchange energies of Heusler compounds, a substantially smaller dataset, the improvement is reduced,indicating that pDOS augmentation is most effective when the training data exceeds the length of the pDOS feature vector. We introduce an interpretable spectral attention-gating mechanism that reveals that the model autonomously learns to prioritize the orbital channels and energy windows most physically relevant to each target property. These results establish pDOS-augmented graph nodes as a broadly applicable strategy for infusing first-principles electronic-structure knowledge into graph networks, opening a practical route to high-accuracy property prediction in data-scarce regimes.