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arXiv2026

Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

cs.LG↗

arXiv2026

Physics-Guided Concentration Inference from Resistance Transients in a Mixed-Phase SnO-SnO$_2$ Carbon Monoxide Sensor with p-n Switching

This work presents a physics-guided machine-learning framework for carbon monoxide concentration inference from experimentally measured resistance transients of a mixed-phase SnO-SnO$_2$ material gas sensor exhibiting temperature-dependent p-n switching behavior. Cycle-level transient responses are represented through physically interpretable descriptors and complemented by compact fast Fourier transform (FFT) and discrete wavelet transform (DWT)-based summaries. Using leakage-aware grouped cross-validation, we study both multi-class concentration classification and continuous concentration regression for the p-type and n-type sensing regimes separately. Across both regimes, fused features provide the strongest overall performance, while the physics-guided descriptor block remains highly competitive, indicating that the dominant concentration information is already encoded in physically meaningful transient dynamics. The p-type branch shows the best concentration-class discrimination, with the fused Random Forest classifier reaching approximately $96.5\%$ accuracy, whereas the n-type branch yields the best quantitative concentration estimation, with the fused Random Forest regressor achieving an MAE$\approx 1.48$ ppm and an R$^2$ $\approx 0.992$. These results reveal a clear dual-regime behavior: p-type sensing is particularly favorable for classification, whereas n-type sensing is more favorable for high-fidelity regression. More broadly, the study demonstrates that leakage-aware, cycle-level, physics-guided machine learning can extend conventional gas-sensing analysis beyond single-response metrics while preserving physical interpretability

physics.chem-ph↗

arXiv2026

Constrained dynamics for searching saddle points on embedded Riemannian submanifolds of Euclidean space

Finding constrained saddle points on embedded Riemannian submanifolds of Euclidean space is significant for analyzing energy landscapes arising in physics and chemistry. Existing works exploit explicit global/local regular level-set representations of manifolds, which may be unavailable or computationally inconvenient for manifolds represented through, e.g., projectors, factorizations, or rank constraints. In this paper, we develop a constrained saddle dynamic based on embedded-submanifold geometric primitives, completely avoiding the use of explicit representations. In particular, our dynamic is formulated compactly on the Grassmann bundle of the tangent bundle. By analyzing the Grassmann bundle geometry, we rigorously establish the local linear stability of the dynamic and the local linear convergence of the resulting algorithms. Remarkably, our analysis provides the first iterate convergence result for discretized algorithms to saddle points of prescribed indices in embedded-submanifold settings. Moreover, by virtue of the Grassmann bundle formulation, we remove unnecessary nondegeneracy assumptions on the eigenvalues of the Riemannian Hessian that are present in existing works. We also point out that locating saddle points can be more ill-conditioned than finding local minimizers, and requires using nonredundant parametrizations. Finally, numerical experiments on linear eigenvalue problems and electronic excited-state calculations showcase the effectiveness of the proposed algorithms and corroborate the established local theory.

math.NA↗

arXiv2026

Polarizable atomic multipoles for learning long-range electrostatics

Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, physically meaningful electrical responses emerge without direct supervision. The learned latent multipoles yield accurate Born effective charge tensors and infrared spectra in close agreement with experiments. The induced-dipole extension introduces new capabilities: it predicts polarizabilities and thereby enables semi-quantitative Raman spectra for bulk water and hybrid MAPbI$_3$ perovskite, as well as the essential features of the surface-specific vibrational sum-frequency generation spectrum at the water-air interface. In ferroelectric HfO$_2$, the predicted electrical response also captures LO-TO splitting and polarization switching. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.

cond-mat.mtrl-sci↗

arXiv2026

Separating perception from reasoning in vision-language models: a model-free render ceiling for crystal structures

Multimodal evaluations cannot say whether a vision-language model misread an image or misreasoned about it, because every existing method for separating the two places a second model in the loop. We introduce the render ceiling, a model-free reference for benchmarks built by rendering known objects: inverting the frozen cameras and re-solving cross-view correspondence recovers exactly the answer the images support. We prove the ceiling fails only through an enumerable set of projection coincidences and certify that set empty on 2,160 rendered crystal structures, so every point of a model's deficit belongs to the model. Across fourteen vision-language models, supplying exact geometry as text lifts every model yet closes under half the gap for thirteen, while a supervised vision model with no language component reads the same images at 0.8952, above every vision-language model. The instrument exposes extraction-stage fabrication that downstream accuracy would misattribute to reasoning, yields camera-placement rules for benchmark builders, and transfers to any benchmark with an invertible forward rendering.

cs.CV↗

arXiv2026

HiPoly: a hierarchical polymer-native AI framework for property prediction and generative design

Polymeric materials are central to modern technologies, with applications ranging from energy to health and transportation. Although AI has made significant advances in materials discovery, the hierarchical structure of polymers across multiple length scales makes them inherently difficult to represent in a unified and physically meaningful way. Here we introduce HiPoly, a polymer-native AI framework that processes complete polymer descriptions through a three-level hierarchical graph architecture built on the G2RINS representation. HiPoly encodes stochastic inter-monomer connectivity, composition, and molecular weight directly within its architecture, using physically motivated design principles that mirror the multi-scale nature of polymeric systems. The framework establishes an end-to-end AI-driven workflow from experimental formulation data to property prediction, generative molecular design, and physics-based validation through molecular simulations, all unified by a single polymer representation. We demonstrate state-of-the-art prediction accuracy for thermophysical properties of multi-component polymer systems, with ablation studies confirming that each hierarchical design choice contributes independently to model performance. As an example, the generative design pathway is applied here to the discovery of sustainable alternatives to persistent fluorinated polymers, where it is possible to identify and independently validate PFAS-free candidates with target surface-energy properties. This work demonstrates how polymer-native AI can accelerate discovery by linking representation, prediction, and design across complex polymer chemistries.

physics.chem-ph↗

arXiv2026

Hessian-based molecular conformation augmentation for a scalable and efficient strategy of machine learning interatomic potentials

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet, standard MLIPs tend to be trained on energy and forces alone, leaving Hessian information largely unexploited. Meanwhile, existing methods that explicitly incorporate the Hessian into training objectives require architectural modifications and introduce significant computational and memory overheads due to higher-order backpropagation. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (\textbf{UniAug}) and normal mode-weighted displacement (\textbf{ModeAug}). Both methods utilize simple Taylor expansions, achieving effective augmentation without altering training objectives or extending the autograd graph. This allows seamless, plug-and-play integration with existing architectures and training pipelines. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy while providing practical, task-specific guidelines.

cs.LG↗

arXiv2023

Information geometric bound on general chemical reaction networks

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

physics.chem-ph↗

arXiv2026

Recovering molecules from coarse-grained beads: free-energy-conditioned generative backmapping across chemical space

Transferable coarse-grained (CG) force fields compress chemical space: by aggregating atoms into a reduced set of interaction beads, models such as MARTINI reduce the number of distinguishable compounds by roughly three orders of magnitude, making high-throughput screening of thermodynamic properties tractable across soft matter, with drug--membrane permeability as a well-developed example. The compression is lossy and, so far, one-way: a screen returns a combination of beads, with no established route back to the compounds it stands for. Recovering those compounds--compositional backmapping--is a one-to-many inverse map, distinct from the better-studied conformational problem of rebuilding atomic coordinates from a known mapping. Here we formulate compositional backmapping as conditional graph generation by introducing juniper, a discrete denoising diffusion model over molecular graphs conditioned on the octanol--water partition free energy $ΔG_{\mathrm{W} \mapsto \mathrm{O}}$, the principal driver of MARTINI bead type assignment and hence a proxy for bead identity. Trained on molecules of up to 9 heavy atoms mapped onto one or two beads, juniper generates molecules that are 93\% valid and 92\% unique for two-bead targets, and whose $ΔG_{\mathrm{W} \mapsto \mathrm{O}}$ distributions track the target $ΔG^{\mathrm{CG}}_{\mathrm{W} \mapsto \mathrm{O}}$ linearly ($r^{2} \geq 0.96$), departing only in the hydrophobic and hydrophilic tails. Although the model receives no chemical information beyond a single scalar, the functional groups shift systematically with the imposed free energy, from branched hydrocarbons at the apolar end to amides, imides, and isocyanates at the polar end. A bead combination flagged by a CG screen can therefore be turned into candidate molecules for atomistic study or synthesis.

physics.chem-ph↗

arXiv2026

Latent unified smooth Hamiltonians for excited state chemistry

We describe a neural network architecture and training procedure designed to model electronic ground and excited states of arbitrary molecular systems. By indirectly learning a latent, implicit basis representation of the electronic-state Hamiltonian, the model offers a unified treatment of multiple electronic states, conical intersections, and non-adiabatic couplings. The formalism can be further extended to learn consistent latent representations of additional operators such as transition dipole moments, for example. To demonstrate the general capabilities of our architecture, we train and evaluate networks on two realistic photochemical systems, thymine and azobenzene. The resulting models accurately reproduce energies and oscillator strengths for the ground- and low-lying excited states relevant to the photochemistry of these systems. We highlight the performance of the trained networks by studying critical molecular geometries, including conical intersections and excited state minima. By construction, the proposed framework also recovers the emergence of Berry phase accumulation around conical intersections. By pairing key mathematical structure from quantum chemistry with the representation learning power of transformers, the presented architecture offers a qualitatively new path toward fast and accurate ground- and excited-state simulations.

physics.chem-ph↗

arXiv2026

Quantum matrix arithmetics with Hamiltonian evolution

The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a Hamiltonian -- using Hamiltonian evolutions of input operators. We show how to maintain this $\textit{Hamiltonian block encoding}$, so that matrix operations can be composed one after another, and the entire quantum computation takes $\leq 2$ ancilla qubits. We achieve this for matrix multiplication, matrix addition, matrix inversion, Hermitian conjugation, fractional scaling, integer scaling, complex phase scaling, as well as singular value transformation for both odd and even polynomials. We also present an overlap estimation algorithm to extract classical properties of Hamiltonian block encoded operators, analogous to the well known Hadamard test, at no extra cost of qubit. Our Hamiltonian matrix multiplication uses the Lie group commutator product formula and its higher-order generalizations due to Childs and Wiebe. Our Hamiltonian singular value transformation employs a dominated polynomial approximation, where the approximation holds within the domain of interest, while the constructed polynomial is upper bounded by the target function over the entire unit interval. We describe a circuit for simulating a class of sum-of-squares Hamiltonians, attaining a commutator scaling in step count, while leveraging the power of matrix arithmetics to reduce the cost of each simulation step. In particular, we apply this to the doubly factorized tensor hypercontracted Hamiltonians from recent studies of quantum chemistry, obtaining further improvements for initial states with a fixed number of particles. We achieve this with $1$ ancilla qubit.

quant-ph↗

arXiv2026

AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.

cs.LG↗

arXiv2026

Unraveling the PFAS helix: A statistical approach

The extreme persistence of per- and polyfluoroalkyl substances (PFAS) in the environment is rooted in their three-dimensional molecular conformation. The helical twist adopted by perfluoroalkyl chains due to hyperconjugation involving their recalcitrant C-F bonds governs their resistance to degradation, yet a quantitative, continuous metric for helicity has remained absent. Here we introduce a data-driven framework that quantifies backbone helicity using three statistical descriptors: void-state (binary occupancy) spatial autocorrelations, local backbone principal component analysis, and persistent homology. We further validate each statistical descriptor against geometric dihedral benchmarks and DFT-calculated Vibrational Circular Dichroism (VCD) spectra. The framework is initially established on a homologous series of perfluorocarboxylic acids (FC2 through FC16) and their hydrogenated analogues, then extended across perfluorosulfonic acids, fluorotelomer alcohols, polyfluoroalkyl hexanoic acid analogues, and longer-chain PFOA and PFOS analogues. Agreement between statistical, geometric, and spectroscopic definitions of helicity is established for PFCAs and extended to structurally distinct subfamilies, including PFOA analogues of varying fluorine content and perfluorosulfonic acids, demonstrating that the descriptors are robust to changes in headgroup chemistry and fluorine substitution pattern. The framework provides a chemistry-agnostic toolset for incorporating backbone conformation into predictive models of PFAS environmental fate and degradation reactivity.

physics.chem-ph↗

arXiv2026

MakoXC: Rearchitecting DFT Exchange-Correlation with Matrix-Aligned and Knowledge-Organized Sparsity

Density Functional Theory (DFT) is indispensable for materials science and drug discovery, yet the exchange--correlation (XC) evaluation remains a major bottleneck due to its cubic scaling. Although linear-scaling methods exploit electronic nearsightedness to reduce asymptotic complexity, they produce irregular sparse workloads that hide implicit sparsity and prevent efficient use of modern AI accelerators. We present MakoXC, a modular matrix-aligned XC evaluation engine that rearchitects nearsightedness-induced sparsity into regular, accelerator-friendly computations. MakoXC co-designs three key techniques: (1) Matrix-Aligned Cells reorganize nearsightedness-induced interactions into dense, accelerator-aligned data clusters; (2) Sparsity-Guided Activation translates deeper implicit sparsity into numerically correct structured execution for practical linear scaling; and (3) Kernel-Fused Pipeline consolidates fragmented workloads into a unified, compute-intensive execution path that fully unleashes accelerator throughput. Extensive evaluations show that MakoXC achieves average speedups of 67.8$\times$ speedup over standard XC evaluation and 4.7$\times$ over state-of-the-art linear-scaling methods. When integrated into a production-grade commercial DFT package, MakoXC scales XC evaluation to ubiquitin (1,231 atoms, def2-SVP) on 64 GPUs, enabling the end-to-end DFT calculation to complete in under five minutes. By restructuring XC evaluation into a unified, structured computation, MakoXC demonstrates how scientific workloads can achieve genuine low complexity while maximizing parallel efficiency on AI accelerators.

cs.DC↗

arXiv2026

Prototype-guided transfer of sparse literature knowledge for electrolyte additive discovery

Electrolyte additive discovery remains challenging because experimentally validated molecules are sparse, whereas accessible chemical spaces are vast and largely unlabeled. This challenge is amplified in lithium-ion batteries, where additive performance arises from coupled interfacial reactions rather than a single molecular property. Here, we develop a prototype-guided molecular intelligence, ProtoMI, a literature-driven framework that learns transferable structural priors from reported electrolyte additives and uses them to prioritize candidates in unlabeled chemical space. For boron-containing additives, ProtoMI combines 126 literature-reported molecules with 179,977 unlabeled candidates. Graph contrastive learning identifies seven chemically interpretable prototypes from the reported additives, and prototype guided semi-supervised contrastive learning adapts these prototypes to the candidate space under source-target distribution mismatch. In retrospective temporal validation, ProtoMI achieves enrichment factors of 9.2-45.6 while screening less than 2% of the candidate space. A subsequent translation step identifies four commercially accessible candidates. One representative candidate, 4,4,5,5-Tetramethyl-2-[10-(1naphthyl)anthracen-9-yl]-1,3,2-dioxaborolane (TNDB), improves high-temperature LiFePO4||graphite cycling at 55 °C by 34.93% relative to the baseline electrolyte. An arsenal of characterizations and operando optical fiber Fourier transform infrared spectroscopy suggest that TNDB forms B-containing, F/P/O-modified inorganic interphases, suppresses solvent decomposition and reduces Fe deposition on graphite. This case study shows how sparse literature knowledge can guide experimentally efficient molecular discovery in data-scarce battery-additive spaces.

physics.chem-ph↗

arXiv2026

La Agente Óptima: Towards Agentic Self-Driving Laboratories

Self-driving laboratories (SDLs) combine automated experimentation with adaptive decision-making to accelerate scientific discovery. Their operation nevertheless often depends on human specialists who translate scientific objectives into executable closed-loop campaigns. Specialists adjust them as data and operating conditions change. Here, we present La Agente Óptima, an agentic framework that constructs and supervises Bayesian optimization campaigns across computational and experimental systems while maintaining a persistent optimization state. By separating large language model (LLM) reasoning from executed campaigns, Óptima runs repetitive optimization loops consistently, returns control to the agent only when progress requires interpretation or campaign revision, and keeps every decision auditable. We evaluate Óptima across ablation studies, five digital discovery tasks, and two physical platforms. Throughout, Óptima maintained executable campaigns as both the scientific problem and execution environment evolved. In a closed-loop contact angle optimization campaign, Óptima identified and corrected a mid-run measurement failure, bringing the contact angle from 71.4 to 67.8 degrees, just above the 64-66 degree range. From this result, Óptima correctly inferred that the target was likely unattainable with the available reagents and recommended changing the formulation. In a five-day multi-objective flow-chemistry campaign, Óptima increased the yield from 30% to 59% over 23 experiments. Despite substantial inference costs, it cost less and used substantially less starting material than a human-directed campaign, while selecting a more mass-efficient operating point. These results show that LLM-based agents can make rigorous, long-running optimization campaigns accessible to domain scientists without specialist setup, expanding the scope of SDLs.

cs.AI↗

arXiv2026

Geometric integrators for adiabatically closed simple thermodynamic systems

A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework for thermodynamic systems, recovering the evolution equations obtained variationally. In this paper, we develop a discrete variational principle for adiabatically closed simple thermodynamic systems, which can be utilised to construct numerical integrators for the dynamics of such systems. The effectiveness of our method is illustrated with several examples.

math-ph↗

arXiv2026

Functional Connectivity Networks for Transportation Delay Analysis: from Theory to Software

Within the endeavour of modelling and understanding the propagation of delays in transportation networks, an approach that has attracted increasing interest in the last decade is the creation of functional network representations. These graphs map elements of interest (e.g. airports or stations) as nodes, and derive pairwise propagation patterns from their dynamics through correlation and causality tests. In spite of multiple notable results, this approach still lacks a coherent framework, with decisions related to many fundamental steps being left to the judgement of the researcher. We here provide an introduction to the theory behind functional networks for transportation systems, detailing the main steps and the associated pitfalls. We further introduce a Python package, delaynet, designed to support the researcher in the reconstruction and analysis of such networks. We finally present an analysis of the propagation of delays in the Swiss train system; and discuss future research steps.

physics.soc-ph↗