Miha Rot, Gregor Kosec
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency. Meshless methods approximate differential operators based on the values of the field in computational nodes, offering a natural approach to adaptivity. The density of computational nodes can either be increased to enhance accuracy or decreased to reduce the number of numerical operations, depending on the properties of the intermediate solution. In this paper, we utilise an adaptive discretisation approach for the numerical simulation of natural convection in non-Newtonian fluid flow. The shear-thinning behaviour is interesting both due to its numerous occurrences in nature, blood being a prime example, and due to its properties, as the decreasing viscosity with increasing shear rate results in sharper flow structures. We focus on the de Vahl Davis test case, a natural convection driven flow in a differentially heated rectangular cavity. The thin boundary layer flow along the vertical boundaries makes this an ideal test case for refinement. We demonstrate that adaptively refining the node density enhances computational efficiency and examine how the parameters for adaptive refinement affect the solution.
Po-Yen Lai, Xinyu Yang, Derrick Low, Huizhe Liu, Jian Cheng Wong
In response to the urban heat island effects and building energy demands in Singapore, this study proposes an agentic AI-enabled reasoning framework that integrates large language models (LLMs) with lightweight physics-based models. Through prompt customization, the LLMs interpret urban design tasks, extract relevant policies, and activate appropriate physics-based models for evaluation, forming a closed-loop reasoning-action process. These lightweight physics-based models leverage core thermal and airflow principles, streamlining conventional models to reduce computational time while predicting microclimate variables, such as building surface temperature, ground radiant heat, and airflow conditions, thereby enabling the estimation of thermal comfort indices, e.g., physiological equivalent temperature (PET), and building energy usage. This framework allows users to explore a variety of climate-resilient building surface strategies, e.g., green façades and cool paint applications, that improve thermal comfort while reducing wall heat gain and energy demand. By combining the autonomous reasoning capacity of LLMs with the rapid quantitative evaluation of lightweight physics-based models, the proposed system demonstrates potential for cross-disciplinary applications in sustainable urban design, indoor-outdoor environmental integration, and climate adaptation planning. The source code and data used in this study are available at: https://github.com/PgUpDn/urban-cooling-agent.
Wancheng Zhang, Zhenhua Zhang, Rui Xiong, Zhihong Lu
The room-temperature altermagnet \mathrm{KV_2Se_2O} possesses nearly orthogonal flat Fermi surfaces, which in an idealized $d$-wave limit enable complete spin-channel separation and a theoretical charge-to-spin conversion efficiency (CSE) of 100%. Realistic samples, however, host residual elliptical Fermi pockets that enhance charge conductivity while suppressing spin conductivity, drastically reducing the CSE. Here we show that in-plane equibiaxial tensile strain systematically eliminates these parasitic pockets, restoring the flat-band geometry. Our first-principles calculations reveal that the CSE increases monotonically with strain, reaching a record value of approximately 96% at 4% strain. An effective tight-binding model fitted to the computed band structure accurately captures the evolution of the Fermi surface and confirms that the suppression of the pockets -- governed by reduced next-nearest-neighbor hoppings -- is the dominant mechanism for the strain-enhanced CSE. We further identify an unconventional out-of-plane spin current that emerges under tilted electric fields and achieves a CSE of nearly 55% at optimal orientations, offering a promising pathway for field-free perpendicular magnetization switching. Our work establishes strain engineering as a practical route to approach the ultimate conversion limit in altermagnets and provides a design principle for high-efficiency spintronic devices.
Jian Cheng Wong, Isaac Yin Chung Lai, Pao-Hsiung Chiu, Chin Chun Ooi, Abhishek Gupta, Yew-Soon Ong
Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to learn physical outcomes reasonably well. However, current PINN approaches struggle to predict or solve new PDEs effectively when there is a lack of training examples, indicating they do not generalize well to unseen problem instances. In this paper, we present a transferable learning approach for PINNs premised on a fast Pseudoinverse PINN framework (Pi-PINN). Pi-PINN learns a transferable physics-informed representation in a shared embedding space and enables rapid solving of both known and unknown PDE instances via closed-form head adaptation using a least-squares-optimal pseudoinverse under PDE constraints. We further investigate the synergies between data-driven multi-task learning loss and physics-informed loss, providing insights into the design of more performant PINNs. We demonstrate the effectiveness of Pi-PINN on various PDE problems, including Poisson's equation, Helmholtz equation, and Burgers' equation, achieving fast and accurate physics-informed solutions without requiring any data for unseen instances. Pi-PINN can produce predictions 100-1000 times faster than a typical PINN, while producing predictions with 10-100 times lower relative error than a typical data-driven model even with only two training samples. Overall, our findings highlight the potential of transferable representations with closed-form head adaptation to enhance the efficiency and generalization of PINNs across PDE families and scientific and engineering applications.
Sebastian Celis Sierra, Meruyert Khamitova, Ran Zhao, Sadeed Bin Sayed, Hakan Bagci
A thin-sheet (TS) volume integral equation (VIE) formulation incorporating generalized sheet transition conditions (GSTCs) is presented for the simulation of three-dimensional (3D) bianisotropic metasurfaces. The metasurface is represented as an equivalent TS, with its constitutive tensors derived from the GSTC susceptibility tensors. Invoking the TS approximation, the governing VIEs are reduced to surface integral equations (SIEs), in which tangential and normal flux density components are treated as distinct sets of unknowns and discretized using Rao-Wilton-Glisson and pulse basis functions, respectively. In contrast to conventional GSTC approaches based on conventional SIEs, which represent only tangential fields, the proposed framework rigorously enforces the bianisotropic GSTCs, including normal field interactions, while retaining the flux-based VIE character of the formulation. Numerical examples demonstrate the accuracy and robustness of the proposed TS-VIE-GSTC solver for polarization rotation, perfect reflection, multi-directional attenuation, and oblique phase-shift transformation.
Lukas Müllender, Berk Hess, Erik Lindahl
Neural network potentials (NNPs) are rapidly changing the landscape of state-of-the-art molecular dynamics (MD) simulations. To make full use of this development, the community needs flexible, easy-to-use interfaces firmly integrated with existing methodologies. To address this, we here present an interface for hybrid machine learning/molecular mechanics (ML/MM) simulations implemented in the widely used MD code GROMACS. The interface enables NNPs trained in the PyTorch framework to contribute energies and forces during MD simulations, either for selected subsets or entire molecular systems. By defining a flexible set of model inputs and outputs, the interface is agnostic to specific NNP architectures and can accommodate a wide range of descriptor-based and message-passing models. In particular, the design integrates NNP inference seamlessly into the extensive GROMACS molecular simulation ecosystem, providing users with the capability to straightforwardly combine NNPs with existing advanced sampling and free energy workflows. We demonstrate the capabilities of the interface using several representative applications, including enhanced sampling of peptide torsional free energy landscapes, absolute solvation free energy calculations, and protein--ligand simulations. We also run performance benchmarks on water boxes for several different NNP architectures. Our interface is available in recent GROMACS releases, and we believe it will provide a practical foundation for incorporating machine learning potentials into production MD simulations of biomolecular systems.
James Hipperson, Jonathan Hargreaves, Trevor Cox
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial neural networks with millions or billions of parameters is achieved using automatic differentiation frameworks such as JAX and Pytorch. Because these frameworks provide accelerated numerical linear algebra with automatic gradient tracking, they also enable differentiable implementations of numerical methods to be built. This facilitates faster gradient-based optimisation of geometry and materials, as well as solution of inverse problems. We demonstrate JAX-BEM, a differentiable Boundary Element Method (BEM) solver, showing that it matches the error of existing BEM codes for a benchmark problem and enables gradient-based geometry optimisation. Although the demonstrated examples are for acoustic simulations, the concept could be readily extended to electromagnetic waves.
Jiang Zhou, Ziru Deng, Pengcheng Hou
We present a Monte Carlo study of the fractal geometry of clusters formed by discrete-time simple random walks (sRW) of $L^2$ steps on a periodic square $L\times L$ lattice. We verify with high precision that the asymptotic behavior of the cluster mass follows $M/L^2 \simeq (\ln L)^{-1} [\fracπ{2}+b (\ln L)^{-2}]$, with $b\approx -(π/2)^{-2}$, demonstrating marginal ``logarithmic fractals". We further determine the fractal dimension of the hull to be $d_{\rm hull}=1.333\,29(14)=4/3$, in excellent agreement with the prediction of Schramm-Loewner evolution ($\rm SLE_{8/3}$) for the Brownian frontier universality class. More importantly, we analyze the chemical distance $S$ spanning the cluster and obtain strong evidence that it asymptotically scales as $S\sim L(\ln L)^{1/4}$, lying exactly on the theoretical upper bound for the chemical distance for level-set percolation clusters on the two-dimensional Gaussian free field. Our numerical results show that the sRW cluster exhibits a conformally invariant external frontier and contains highly efficient asymptotically linear connective paths.
Yao Luo
The Müller boundary integral equation for penetrable electromagnetic scattering is conventionally discretized using divergence-conforming basis functions, a restriction inherited from the PMCHWT framework. This paper demonstrates that this constraint can be bypassed. The double-gradient operator in the Müller formulation acts on the kernel difference $\varphi_a - \varphi_i$, so that the $\mathcal{O}(R^{-3})$ hypersingularity cancels identically, reducing the operators to weakly singular $\mathcal{O}(R^{-1})$ kernels. Exploiting this cancellation, we develop a nodal, high-order Galerkin formulation using $\mathrm{P}_2$ isoparametric shape functions on curved manifolds. The surface vector field is constructed via a metric-weighted orthonormal tangent frame. The singular integrals are evaluated by Sauter--Schwab quadrature, and a Morton-ordered Block Jacobi preconditioner is introduced. By capturing the dominant near-field interactions within geometrically clustered diagonal blocks, it yields robust, superlinear GMRES convergence under extreme material and geometric parameters. Validation against semi-analytical EBCM references confirms high-order spatial accuracy and optical-theorem satisfaction to high precision.
Aditya Sai Pranith Ayapilla, Kazuya Miyashita, Yuki Yasuda, Ryo Onishi
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive because it requires repeated high-resolution (HR) forecasts and large ensembles. In this study, we develop DiffSRDA, a probabilistic spatiotemporal super-resolution data assimilation framework based on denoising diffusion models, and evaluate it on an idealized barotropic ocean jet instability testbed. DiffSRDA is trained offline to generate short HR analysis windows conditioned on (i) a time series of low-resolution (LR) forecast frames and (ii) sparse HR observations. Repeated reverse diffusion sampling then produces an ensemble of HR analyses, providing both point estimates and uncertainty information. Despite relying only on low-cost LR forecasts, DiffSRDA achieves reconstruction quality close to that of an Ensemble Kalman Filter (EnKF) driven by HR forecasts, while improving over deterministic CNN-based SRDA baselines. The sampled ensemble also yields physically meaningful uncertainty patterns, with spread concentrated in dynamically active regions similarly to EnKF. A key practical result is that accurate base DiffSRDA cycling does not require long reverse chains: most of the full-chain accuracy is retained with only a few reverse steps, making diffusion-based SRDA practical for repeated cycling. Finally, by exploiting the score-based structure of diffusion sampling, we demonstrate training-free observation-consistency guidance for deployment-time sensor-layout shifts, enabling improved use of changed observation configurations without retraining. Overall, diffusion models provide a practical, uncertainty-aware, and computationally efficient approach for spatiotemporal SRDA in chaotic fluid flows.
Arun Mannodi-Kanakkithodi, Menglin Huang, Prashun Gorai, Seán R. Kavanagh
Point defects in solid-state materials are now routinely simulated using large supercell structures, requiring efficient quantum mechanical solutions. Data-driven and machine learning (ML) models trained on computational data can enable rapid defect property predictions and high-throughput screening. In this article, we provide an overview of prominent efforts to accelerate defect simulations using these approaches. We begin by discussing the motivations for data-driven techniques in defect modeling, and describe efforts over the past decade to use descriptor-based models for rapid screening of defect properties -- most notably in oxides. In particular, we discuss case studies where surrogate models and interatomic potentials were trained on density functional theory (DFT) data, leading to predictions with quantum-mechanical accuracies at a fraction of the cost. In addition to geometry relaxation and formation energy predictions, these interatomic potentials are capable of predicting phonon modes and vibrational free energies to yield defect energetics at finite temperatures -- representing a key frontier for computational defect research. We finish with a discussion on how to connect these approaches and their outputs with experimental data, and provide an outlook on this burgeoning sub-field.
Haobo Yang, Qiu Yang
The Madden-Julian Oscillation (MJO) is a planetary-scale convective system characterized by large-scale envelopes of enhanced and suppressed convection that contain numerous mesoscale convective systems (MCSs). While MCSs are widely recognized as the fundamental convective elements embedded within the MJO, their relationship with the MJO is intrinsically two-way: the MJO modulates the large-scale dynamical and thermodynamic environment that organizes MCS activity, while the collective upscale impacts of MCSs feed back onto the MJO through the transport of momentum and heat. However, the nature of this bidirectional interaction remains insufficiently quantified from an observational perspective. In this study, we use satellite-based MJO indices together with a long-term, objectively tracked MCS dataset to investigate the two-way feedback mechanisms between the MJO and MCSs. By compositing MCS activity across different MJO phases and analyzing their environmental conditions, we quantify how the evolving MJO circulation regulates MCS frequency, intensity, and organization. At the same time, we diagnose the aggregate influence of MCS populations on the large-scale MJO circulation through their associated momentum and thermodynamic anomalies. Our results reveal a robust two-way coupling between the MJO and MCSs. Enhanced MCS activity preferentially occurs in specific MJO phases associated with favorable moisture, instability, and vertical shear, indicating strong MJO control on MCS organization. Conversely, periods of enhanced MCS activity are associated with coherent large-scale circulation anomalies consistent with upscale transport of momentum and moisture that reinforce the MJO convective envelope and support its eastward propagation. This feedback suggests that MCSs are not merely passive responses to the MJO environment, but actively contribute to its maintenance and evolution.
Huaiping Wang, Qiu Yang
Mesoscale convective systems MCSs play a central role in tropical rainfall and are closely linked to extreme precipitation and large scale variability. However, a quantitative understanding of their environmental controls remains incomplete. In this study, we construct an observational MCS dataset by applying an objective tracking algorithm to satellite and reanalysis data, and examine the climatology of tropical MCSs. We further use a Random Forest model to quantify environmental controls at the monthly scale. The results show pronounced spatial and seasonal variability in tropical MCS activity, closely tied to large scale circulation and moisture availability. Environmental predictors explain up to about 50\% of the variance in monthly MCS frequency and associated precipitation. Moisture convergence atmospheric instability and column integrated water vapor emerge as the leading controlling factors. Partial dependence analyses reveal clear nonlinear interactions among key predictors. The relative importance of environmental controls also varies with region and season, with thermodynamic factors dominating in some regimes and dynamic factors such as vertical wind shear playing a larger role in others. Overall, this study provides an observationally constrained quantification of environmental controls on tropical MCSs and offers new insight into their variability and potential response to climate variability and change.
Saptarshi G. Dastider, K. Prashant, P. Shruti, C. Sudheesh, Jobin Cyriac
Accurate modeling of ion-molecule reaction networks is essential for understanding the chemical evolution of planetary ionospheres, particularly for giant planets where proton-transfer chains drive atmospheric composition. However, predicting reaction rates in these ultracold environments remains a challenge due to the non-trivial interplay between vibrational dynamics and quantum tunneling. In this work we present a chaos-diagnostic framework that integrates multireference electronic structure theory, Adiabatic Gauge Potentials (AGP), and Random Matrix Theory (RMT) to characterize the microscopic dynamics of proton transport. Using the formation of H+3 and the proton-bound cluster H+5 as representative model systems relevant to Jovian atmospheres, we demonstrate that the transition state acts as a dynamical bottleneck where quantum chaos is notably suppressed, effectively enhancing tunneling probabilities. We introduce a fragility index based on the AGP slope to quantify how specific vibrational modes reintroduce chaos and suppress reactivity. This diagnostic approach offers a generalizable, data-driven metric for identifying vibrationally gated pathways in complex astrochemical networks, providing a theoretical basis for refining kinetic models of planetary and interstellar plasmas
Peter Collett, Alexander Johannes Stasik, Simone Casolo, Signe Riemer-Sørensen
Accurate condition monitoring of industrial equipment requires inferring latent degradation parameters from indirect sensor measurements under uncertainty. While traditional Bayesian methods like Markov Chain Monte Carlo (MCMC) provide rigorous uncertainty quantification, their heavy computational bottlenecks render them impractical for real-time process control. To overcome this limitation, we propose an AI-driven framework utilizing Simulation-Based Inference (SBI) powered by amortized neural posterior estimation to diagnose complex failure modes in heat exchangers. By training neural density estimators on a simulated dataset, our approach learns a direct, likelihood-free mapping from thermal-fluid observations to the full posterior distribution of degradation parameters. We benchmark this framework against an MCMC baseline across various synthetic fouling and leakage scenarios, including challenging low-probability, sparse-event failures. The results show that SBI achieves comparable diagnostic accuracy and reliable uncertainty quantification, while accelerating inference time by a factor of82$\times$ compared to traditional sampling. The amortized nature of the neural network enables near-instantaneous inference, establishing SBI as a highly scalable, real-time alternative for probabilistic fault diagnosis and digital twin realization in complex engineering systems.
Philip Trøst Kristensen, Thomas Kiel, Kurt Busch, Francesco Intravaia
Surface deformations of optical cavities and plasmonic nanoparticles are inevitable in nanophotonics. The random morphology changes of different realizations modify the associated resonance frequencies and quality factors, which may be characterized by specified distributions instead of their nominal values. As an alternative to statistical analyses based on direct numerical calculations, we present an approximate method using first-order perturbation theory with shifting boundaries. For an example resonator in the form of a plasmonic nanowire, the approach explains the bivariate frequency distribution observed in direct numerical calculations involving 1000 realizations of random surface deformations and provides the average and the associated covariance matrix with relatively high accuracy.
Kirsten I. Tempest, Matthias Beylich, George C. Craig
Artificial Intelligence (AI) weather models are improving rapidly, and their forecasts are already competitive with long-established traditional Numerical Weather Prediction (NWP). To build confidence in this new methodology, it is critical that we understand how these predictions are generated. This is a huge challenge as these AI weather models remain largely black boxes. In other areas of Machine Learning (ML), mechanistic interpretability has emerged as a framework for understanding ML predictions by analysing the building blocks responsible for them. Here we present an open-source, highly adaptable tool which incorporates concepts from mechanistic interpretability. The tool organises internal latent representations from the model processor and allows for initial analyses, including cosine similarity and Principal Component Analysis (PCA), enabling the user to identify directions in latent space potentially associated with meteorological features. Applying our tool to the graph neural network GraphCast, we present preliminary case studies for mid-latitude synoptic-scale waves and specific humidity. These demonstrate the tool's ability to identify linear combinations of latent channels that appear to correspond to interpretable features.
Xiaorong Zou, Hyeon Suk Shin, Chang-Jong Kang, Baibiao Huang, Yanmei Zang, Ying Dai, Chengwang Niu, Chang Woo Myung
The discovery of higher-order topological insulator (HOTI) has established a new paradigm for understanding symmetry-constrained boundary electronic states. Here, based on first-principles calculations, we demonstrate the emergence of HOTI phase in organic lattices of two-dimensional azulenoid-kekulene-type carbon allotropes, namely AKC-[3,3] and AKC-[6,0]. Enabled by the $C_6$ rotational symmetry, the nontrivial bulk topology is confirmed through the topological invariant and fractionally quantized corner charge, giving $\{[M^{(I)}_{2}],[K^{(3)}_{2}]\}$ = $\{0,2\}$ and $Q_{\mathrm{corner}} = e/3$, respectively, accompanied by the emergence of exotic corner states in nanoflakes. Notably, the structural modifications are explored, revealing that in the derived structure PAK-[6,0], whose corner-localized states are preserved, highlighting the robustness of the higher-order topological phase. These findings highlight azulenoid-kekulene-based carbon allotropes as a promising platform to explore the interplay between structural design, crystalline symmetry, and higher-order topological boundary responses in two dimensional carbon systems.
Isabel Nha Minh Le, Roeland Wiersema, Christian B. Mendl
Apr 22, 2026·quant-ph·PDF Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is computationally prohibitive for large-scale systems. In this work, we bypass this bottleneck by introducing an analytical Hessian-vector product kernel designed for arbitrary compositions of linear maps. This two-pass algorithm leverages recursive tangent-state propagation with a bounded virtual bond dimension to guarantee scalability. We demonstrate the practical utility of this kernel by integrating it into a Riemannian trust-region framework for quantum circuit compression. Evaluated on time-evolution circuits for various spin chains, our second-order approach achieves up to a four-order-of-magnitude improvement in fidelity over naive Trotterization, while delivering significantly smoother, faster convergence than conventional first-order methods such as Riemannian ADAM.
Jia-Wen Li, Sheng Meng, Xinghua Shi, Jin Zhang, Wei-Hai Fang
Sliding ferroelectrics built from stacked nonpolar monolayers enable out-of-plane polarization and unconventional switching via interlayer sliding, yet the microscopic sliding dynamics remain unclear. Using machine-learning molecular dynamics, we reveal spontaneous thermally driven interlayer sliding in ferroelectric MoS2 moiré superlattices, with relative velocities on the order of 1 m/s at 300 K. Instead of rigid translation of the entire bilayer, the motion appears as a global drift of the moiré pattern. Such thermally driven sliding is inconsistent with the meV/atom-scale rigid-sliding barrier. In contrast, when constrained relaxation is allowed, the sliding proceeds along an almost barrierless pathway that directly reproduces the global drift of the moiré pattern. Furthermore, sulfur vacancies trigger a sliding-to-pinning transition, with about 0.1% S vacancies already sufficient to convert the long-range sliding into localized oscillations. Notably, these phenomena are not restricted to small twist angles, but arise generically in twisting-induced multidomain structures. These results reveal that the sliding process is governed by a domain-wall-mediated collective reconstruction pathway with an ultralow barrier, rather than rigid layer translation, deepening the understanding of microscopic dynamics in moiré superlattices and sliding ferroelectrics.