CyberSec Research

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this study, we explore the application of PINNs for solving unsteady Maxwell's equations and compare their performance with two established numerical methods: the Finite-Difference Time-Domain (FDTD) method and a compact Pade scheme with filtering. Three benchmark problems are considered, ranging from 1D free-space wave propagation to 2D Gaussian pulses in periodic and dielectric media. We assess the effectiveness of convergence-enhancing strategies for PINNs, including random Fourier features, spatio-temporal periodicity, and temporal causality training. An ablation study highlights that architectural choices must align with the underlying physics. Additionally, we employ a Neural Tangent Kernel framework to examine the spatio-temporal convergence behavior of PINNs. Results show that convergence rates correlate with error over time but not in space, revealing a limitation in how training dynamics allocate learning effort. Overall, this study demonstrates that PINNs, when properly configured, can match or surpass traditional solvers in accuracy and flexibility, though challenges remain in addressing spatial inhomogeneity and adapting training to localized complexity.

Recent developments in computational chemistry facilitate the automated quantum chemical exploration of chemical reaction networks for the in-silico prediction of synthesis pathways, yield, and selectivity. However, the underlying quantum chemical energy calculations require vast computational resources, limiting these explorations severely in practice. Machine learning potentials (MLPs) offer a solution to increase computational efficiency, while retaining the accuracy of reliable first-principles data used for their training. Unfortunately, MLPs will be limited in their generalization ability within chemical (reaction) space, if the underlying training data is not representative for a given application. Within the framework of automated reaction network exploration, where new reactants or reagents composed of any elements from the periodic table can be introduced, this lack of generalizability will be the rule rather than the exception. Here, we therefore study the benefits and drawbacks of two MLP concepts in this context. Whereas universal MLPs are designed to cover most of the relevant chemical space in their training, lifelong MLPs push their adaptability by efficient continual learning of additional data. While the accuracy of the universal MLPs turns out to be not yet sufficient for reaction search trials without any fine-tuning, lifelong MLPs can reach chemical accuracy. We propose an improved learning algorithm for lifelong adaptive data selection yielding efficient integration of new data while previous expertise is preserved.

This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions under varying physical parameters. Solutions are approximated as empirical measures of particles that adaptively align with the high-gradient regions. The core idea of the BDP method is to learn both forward and reverse mappings (between the uniform and a non-trivial target distribution) by minimizing the discrete 2-Wasserstein distance (W2) and optimizing the transition map therein by a minibatch technique. We present numerical results demonstrating the effectiveness of the BDP method for learning and generating solutions to Keller-Segel chemotaxis systems in the presence of laminar flows and Kolmogorov flows with chaotic streamlines in three space dimensions. The BDP outperforms two recent representative single-step flow matching and diffusion models (rectified flow and shortcut diffusion models) in the generative AI literature. However when the target distribution is high-dimensional (4 and above), e.g. a mixture of two Gaussians, the single-step diffusion models scale better in dimensions than BDP in terms of W2-accuracy.

Among the quasi-2D van der Waals magnetic systems, Fe4GeTe2 imprints a profound impact due to its near-room temperature ferromagnetic behaviour and the complex magnetothermal phase diagram exhibiting multiple phase transformations, as observed from magnetization and magnetotransport measurements. A complete analysis of these phase transformations in the light of electronic correlation and its impact on the underlying magnetic interactions remain unattended in the existing literature. Using first-principles methodologies, incorporating the dynamical nature of electron correlation, we have analysed the interplay of the direction of magnetization in the easy-plane and easy-axis manner with the underlying crystal symmetry, which reveals the opening of a pseudogap feature beyond the spin-reorientation transition (SRT) temperature. The impact of dynamical correlation on the calculated magnetic circular dichroism and x-ray absorption spectrum of the L-edge of the Fe atoms compared well with the existing experimental observations. The calculated intersite Heisenberg exchange interactions display a complicated nature, depending upon the pairwise interactions among the two inequivalent Fe sites, indicating a RKKY-like behaviour of the magnetic interactions. We noted the existence of significant anisotropic and antisymmetric exchanges interactions, resulting into a chirality in the magnetic behaviour of the system. Subsequent investigation of the dynamical aspects of magnetism in Fe4GeTe2 and the respective magnetothermal phase diagram reveal that the dynamical nature of spins and the decoupling of the magnetic properties for both sites of Fe is crucial to explain all the experimentally observed phase transformations.

Plasmonic nanostructures provide local field enhancement to be used as efficiency-boosting tools in fluorescence-based applications. For photostable quantum dots (QDs) to have enhanced emission, their size and exact location in the proximity of plasmonic nanostructure become key parameters while constructing light emitting devices. However, plasmonic nanostructures mostly suffer from non-radiative energy transfer at close proximity, which hinders the ultimate performance of fluorophores. In this work, we provided critical interparticle distances through finite difference time domain (FDTD) simulations, where the radiative decay rate is equalized to the non-radiative counterpart for light emitting QD-based technologies. To show the promises of the QD placement at a critical distance, we demonstrate an optical switch for the fluorescence efficiency of a CdSe/ZnS core-shell QD (CSQD) by optically exciting the silver nanoparticle (AgNP) placed at a critical distance. While the provided single particle spectroscopy allows for the observation of heterogeneity in CSQD-AgNP coupling that is often masked in ensemble measurements, our benchmark study serves as a base reference for the development of QD-based light emitting technologies by resolving the optically switchable active tuning of radiative decay rates.

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks represented by Multi-Layer Perceptrons (MLPs). While showing promise, their performance advantages in physics-based problems remain largely unexplored. Several critical questions persist: Can KANs capture complex physical dynamics and under what conditions might they outperform traditional architectures? In this work, we present a comparative study of KANs and MLPs for learning physical systems governed by PDEs. We assess their performance when applied in deep operator networks (DeepONet) and graph network-based simulators (GNS), and test them on physical problems that vary significantly in scale and complexity. Drawing inspiration from the Kolmogorov Representation Theorem, we examine the behavior of KANs and MLPs across shallow and deep network architectures. Our results reveal that although KANs do not consistently outperform MLPs when configured as deep neural networks, they demonstrate superior expressiveness in shallow network settings, significantly outpacing MLPs in accuracy over our test cases. This suggests that KANs are a promising choice, offering a balance of efficiency and accuracy in applications involving physical systems.

Modulating the number of particles in a region is key to accurately capturing the nuances in compressible flows with Smoothed Particle Hydrodynamics (SPH). This paper details the implementation of a volume-based adaptive refinement and derefinement procedure, incorporating state-of-the-art features such as automatic local adaptivity and solution adaptivity. A shock-aware particle shifting procedure is introduced to regularize the particle distribution while preserving the integrity of shocks. To our knowledge, this is the first demonstration of shock-based solution adaptivity and shock-aware particle shifting in the literature. A wide variety of test problems, which involve flow in and around boundaries, are employed to highlight the utility of these adaptivity features in improving the results and in making simulations faster. For instance, the adaptive resolution procedure is shown to deliver an order of magnitude speedup. We also demonstrate the effectiveness of the adaptivity procedure in resolving existing issues like errors due to interaction with differently spaced ghost particles at boundaries, formation of spot-like structures due to particle clumping, and poorly resolved low-density regions. In essence, the adaptivity technique presented in this paper is positioned as a powerful tool for simulating compressible flows with enhanced accuracy and efficiency.

We investigate the role of policy heterogeneity in enhancing the olfactory search capabilities of cooperative agent swarms operating in complex, real-world turbulent environments. Using odor fields from direct numerical simulations of the Navier-Stokes equations, we demonstrate that heterogeneous groups, with exploratory and exploitative agents, consistently outperform homogeneous swarms where the exploration-exploitation tradeoff is managed at the individual level. Our results reveal that policy diversity enables the group to reach the odor source more efficiently by mitigating the detrimental effects of spatial correlations in the signal. These findings provide new insights into collective search behavior in biological systems and offer promising strategies for the design of robust, bioinspired search algorithms in engineered systems.

This works focuses on participation number -- a parameter that allows to quantitatively asses the level of kinetic energy localization. The author presents a clear way of deriving participation number in a continuous case without making any assumptions about the system, fluid or flow regime. Moreover, a method of computing participation number in discretized cases is discussed and verified against well known analytical solutions using three methods, in which one was used previously in research on fluid flow through porous media. A robust formula, that works for both uniform and nonuniform discretization grids is presented.

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods.

We investigate the impact of intercalating a xenon layer between a thin condensed CD4 film of two monolayers (ML) and a platinum surface on the dissociative electron attachment (DEA). The observed desorption results are compared with density functional theory (DFT) calculations, which reveal the binding energies of various anionic and neutral species as a function of the xenon film thickness on the Pt (111) substrate. The theoretical results suggest that 6 ML of xenon are sufficient to diminish the surface effect, enabling physisorbed anionic fragments to desorb from the CD4 film. In contrast, 20 ML (approximately 10 nm) are experimentally necessary to achieve saturation in the desorption of D-. In addition, the presence of xenon layers enables the coupling of resonance states with Xe excited states, thereby inhibiting the electrons from returning to the metal. Aside from reducing surface interactions, the xenon interlayer significantly enhances DEA to CD4.

We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second order time and space derivatives in the IWE are reduced to first order, resulting in a Schr\"odinger equation of motion. Exact diagonalization of the unitary circuit in combination with Tensor Networks allows simulation of the wave equation with a resolution of $10^{13}$ grid points on a laptop. A method for encoding arbitrary analytical functions into diagonal Matrix Product Operators is employed to prepare and evolve a Matrix Product State (MPS) encoding the solution. Since the method relies on the Quantum Fourier Transform, which has been shown to generate small entanglement when applied to arbitrary MPSs, simulating the evolution of initial conditions with sufficiently low bond dimensions to high accuracy becomes highly efficient, up to the cost of Trotterized propagation and sampling of the wavefunction. We conclude by discussing possible extensions of the approach for carrying out Tensor Network simulations of other partial differential equations such as Maxwell's equations.

In machine learning forecasting, standard error metrics such as mean absolute error (MAE) and mean squared error (MSE) quantify discrepancies between predictions and target values. However, these metrics do not directly evaluate the physical and/or dynamical consistency of forecasts, an increasingly critical concern in scientific and engineering applications. Indeed, a fundamental yet often overlooked question is whether machine learning forecasts preserve the dynamical behavior of the underlying system. Addressing this issue is essential for assessing the fidelity of machine learning models and identifying potential failure modes, particularly in applications where maintaining correct dynamical behavior is crucial. In this work, we investigate the relationship between standard forecasting error metrics, such as MAE and MSE, and the dynamical properties of the underlying system. To achieve this goal, we use two recently developed dynamical indices: the instantaneous dimension ($d$), and the inverse persistence ($\theta$). Our results indicate that larger forecast errors -- e.g., higher MSE -- tend to occur in states with higher $d$ (higher complexity) and higher $\theta$ (lower persistence). To further assess dynamical consistency, we propose error metrics based on the dynamical indices that measure the discrepancy of the forecasted $d$ and $\theta$ versus their correct values. Leveraging these dynamical indices-based metrics, we analyze direct and recursive forecasting strategies for three canonical datasets -- Lorenz, Kuramoto-Sivashinsky equation, and Kolmogorov flow -- as well as a real-world weather forecasting task. Our findings reveal substantial distortions in dynamical properties in ML forecasts, especially for long forecast lead times or long recursive simulations, providing complementary information on ML forecast fidelity that can be used to improve ML models.

Modeling and simulation of fluid-structure interactions are crucial to the success of aerospace engineering. This work addresses a novel hybrid algorithm that models the close coupling between compressible flows and deformable materials using a mesoscopic approach. Specifically, the high-speed flows are described by the gas-kinetic scheme, which is a robust Navier-Stokes alternative solver built on the molecular kinetic theory. The deformation, damage, and fracture of materials are depicted using the bond-based peridynamics, which serves as coarse-grained molecular dynamics to construct non-local extensions of classical continuum mechanics. The evolution of fluids and materials are closely coupled using the ghost-cell immersed boundary method. Within each time step, the solutions of flow and solid fields are updated simultaneously, and physics-driven boundary conditions are exchanged for each other via ghost cells. Extensive numerical experiments, including crack propagation in a pre-cracked plate, subsonic flow around the NACA0012 airfoil, supersonic flow around the circular cylinder, and shock wave impacting on the elastic panel, are performed to validate the algorithm. The simulation results demonstrate the unique advantages of current hybrid algorithm in solving fracture propagation induced by high-speed flows.

Understanding the on-chip motion of magnetic particles in a microfluidic environment is key to realizing magnetic particle-based Lab-on-a-chip systems for medical diagnostics. In this work, a simulation model is established to quantify the trajectory of a single particle moving close to a polymer surface in a quiescent liquid. The simulations include hydrodynamic, magnetostatic, and Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions. They are applied to particle motion driven by a dynamically changing magnetic field landscape created by engineered parallel-stripe magnetic domains superposed by a homogeneous, time-varying external magnetic field. The simulation model is adapted to experiments in terms of fluid-particle interactions with the magnetic field landscape approximated by analytic equations under the assumption of surface charges. Varying simulation parameters, we especially clarify the impact of liquid-mediated DLVO interactions, which are essential for diagnostic applications, on the 3D trajectory of the particle. A comparison to experimental results validates our simulation approach.

A large-scale, general-purpose data assimilation (DA) platform for materials modeling, douka, was developed and applied to nonlinear materials models. The platform demonstrated its effectiveness in estimating physical properties that cannot be directly obtained from observed data. DA was successfully performed using experimental images of oxygen evolution reaction at a water electrolysis electrode, enabling the estimation of oxygen gas injection velocity and bubble contact angle. Furthermore, large-scale ensemble DA was conducted on the supercomputer Fugaku, achieving state estimation with up to 8,192 ensemble members. The results confirmed that runtime scaling for the prediction step follows the weak scaling law, ensuring computational efficiency even with increased ensemble sizes. These findings highlight the potential of douka as a new approach for data-driven materials science, integrating experimental data with numerical simulation.

Local neural operator (LNO) conception has provided a feasible way for scientific computations. The LNO learns transient partial differential equations from random field samples, and then the pre-trained LNO solves practical problems on specific computational domains. For applications, we may ask: Are the training samples rich enough? To what extent can we trust the solutions obtained from pre-trained LNO models for unknown cases? The generalizability of LNO could answer these questions. Here, we propose to use two plain scalar features, the amplitude and wavenumber of the input functions, to indicate the richness of training samples and to evaluate the generalization error of pre-trained LNO. In elastodynamic practices, we find that isolated evolving wavenumber modes for Lam\'e-Navier equation caused the training dataset to lack mode diversity. By data supplementation and model fine-tuning targeting to the discovered lack modes, the pre-trained and fine-tuned LNO model solves Lamb problem correctly and efficiently. These results and the proposed generalization criteria provide a paradigm for LNO applications.

The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing in simulating computational fluid dynamics. Many recent works mostly focus on classical simulation, and rely on full state tomography. Several key algorithmic issues like observable readout, data encoding, and impractical circuit depth remain unsolved. As a result, these are not directly realizable on any quantum hardware. We present a series of novel algorithmic advances which allow us to implement the QLBM algorithm, for the first time, on a quantum computer. Hardware results for the time evolution of a 2D Gaussian initial density distribution subject to a uniform advection-diffusion field are presented. Furthermore, 3D simulation results are presented for particular non-uniform advection fields, devised so as to avoid the problem of diminishing probability of success due to repeated post-selection operations required for multiple timesteps. We demonstrate the evolution of an initial quantum state governed by the advection-diffusion equation, accounting for the iterative nature of the explicit QLBM algorithm. A tensor network encoding scheme is used to represent the initial condition supplied to the advection-diffusion equation, significantly reducing the two-qubit gate count affording a shorter circuit depth. Further reductions are made in the collision and streaming operators. Collectively, these advances give a path to realizing more practical, 2D and 3D QLBM applications with non-trivial velocity fields on quantum hardware.