physics.comp-ph

arXiv:2409.19838v2 Announce Type: replace Abstract: Identifying informative low-dimensional features that characterize dynamics in molecular simulations remains a challenge, often requiring extensive manual tuning and system-specific knowledge. Here, we introduce geom2vec, in which pretrained graph neural networks (GNNs) are used as universal geometric featurizers. By pretraining equivariant GNNs on a large dataset of molecular conformations with a self-supervised denoising objective, we obtain transferable structural representations that are useful for learning conformational dynamics without further fine-tuning. We show how the learned GNN representations can capture interpretable relationships between structural units (tokens) by combining them with expressive token mixers. Importantly, decoupling training the GNNs from training for downstream tasks enables analysis of larger molecular graphs (such as small proteins at all-atom resolution) with limited computational resources. In these ways, geom2vec eliminates the need for manual feature selection and increases the robustness of simulation analyses.

arXiv:2501.00003v1 Announce Type: cross Abstract: Nanoparticles (NPs) formed in nonthermal plasmas (NTPs) can have unique properties and applications. However, modeling their growth in these environments presents significant challenges due to the non-equilibrium nature of NTPs, making them computationally expensive to describe. In this work, we address the challenges associated with accelerating the estimation of parameters needed for these models. Specifically, we explore how different machine learning models can be tailored to improve prediction outcomes. We apply these methods to reactive classical molecular dynamics data, which capture the processes associated with colliding silane fragments in NTPs. These reactions exemplify processes where qualitative trends are clear, but their quantification is challenging, hard to generalize, and requires time-consuming simulations. Our results demonstrate that good prediction performance can be achieved when appropriate loss functions are implemented and correct invariances are imposed. While the diversity of molecules used in the training set is critical for accurate prediction, our findings indicate that only a fraction (15-25\%) of the energy and temperature sampling is required to achieve high levels of accuracy. This suggests a substantial reduction in computational effort is possible for similar systems.

arXiv:2501.00011v1 Announce Type: cross Abstract: Atmospheric models demand a lot of computational power and solving the chemical processes is one of its most computationally intensive components. This work shows how to improve the computational performance of the Multiscale Online Nonhydrostatic AtmospheRe CHemistry model (MONARCH), a chemical weather prediction system developed by the Barcelona Supercomputing Center. The model implements the new flexible external package Chemistry Across Multiple Phases (CAMP) for the solving of gas- and aerosol-phase chemical processes, that allows multiple chemical processes to be solved simultaneously as a single system. We introduce a novel strategy to simultaneously solve multiple instances of a chemical mechanism, represented in the model as grid-cells, obtaining a speedup up to 9x using thousands of cells. In addition, we present a GPU strategy for the most time-consuming function of CAMP. The GPU version achieves up to 1.2x speedup compared to CPU. Also, we optimize the memory access in the GPU to increase its speedup up to 1.7x.

arXiv:2501.00015v1 Announce Type: cross Abstract: (Pseudo)random sampling, a costly yet widely used method in (probabilistic) machine learning and Markov Chain Monte Carlo algorithms, remains unfeasible on a truly large scale due to unmet computational requirements. We introduce an energy-efficient algorithm for uniform Float16 sampling, utilizing a room-temperature stochastic magnetic tunnel junction device to generate truly random floating-point numbers. By avoiding expensive symbolic computation and mapping physical phenomena directly to the statistical properties of the floating-point format and uniform distribution, our approach achieves a higher level of energy efficiency than the state-of-the-art Mersenne-Twister algorithm by a minimum factor of 9721 and an improvement factor of 5649 compared to the more energy-efficient PCG algorithm. Building on this sampling technique and hardware framework, we decompose arbitrary distributions into many non-overlapping approximative uniform distributions along with convolution and prior-likelihood operations, which allows us to sample from any 1D distribution without closed-form solutions. We provide measurements of the potential accumulated approximation errors, demonstrating the effectiveness of our method.

arXiv:2501.00016v1 Announce Type: cross Abstract: Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

arXiv:2501.00738v1 Announce Type: cross Abstract: The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing various weather phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can learn effective weather models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension. Moreover, we develop an approach for handling terms that are not integrable-by-parts, such as advection operators.

arXiv:2501.00263v1 Announce Type: new Abstract: In this paper, we propose and implement a structure-preserving stochastic particle method for the Landau equation. The method is based on a particle system for the Landau equation, where pairwise grazing collisions are modeled as diffusion processes. By exploiting the unique structure of the particle system and a spherical Brownian motion sampling, the method avoids additional temporal discretization of the particle system, ensuring that the discrete-time particle distributions exactly match their continuous-time counterparts. The method achieves $O(N)$ complexity per time step and preserves fundamental physical properties, including the conservation of mass, momentum and energy, as well as entropy dissipation. It demonstrates strong long-time accuracy and stability in numerical experiments. Furthermore, we also apply the method to the spatially non-homogeneous equations through a case study of the Vlasov--Poisson--Landau equation.

arXiv:2412.17989v1 Announce Type: new Abstract: Thermal radiative transfer (TRT) is an essential piece of physics in inertial confinement fusion, high-energy density physics, astrophysics etc. The physical models of this type of problem are defined by strongly coupled differential equations describing multiphysics phenomena. This paper presents a new nonlinear multilevel iterative method with two photon energy grids for solving the multigroup radiative transfer equation (RTE) coupled with the material energy balance equation (MEB). The multilevel system of equations of the method is formulated by means of a nonlinear projection approach. The RTE is projected over elements of phase space to derive the low-order equations of different types. The hierarchy of equations consists of (1) multigroup weighted flux equations which can be interpreted as the multigroup RTE averaged over subintervals of angular range and (2) the effective grey (one-group) equations which are spectrum averaged low-order quasidiffusion (aka variable Eddington factor) equations. The system of RTE, low-order and MEB equations is approximated by the fully implicit Euler time-integration method in which absorption coefficient and emission term are evaluated at the current time step. Numerical results are presented to demonstrate convergence of a multilevel iteration algorithm in the Fleck-Cummings test problem with Marshak wave solved with large number of photon energy groups.

arXiv:2412.18263v1 Announce Type: new Abstract: Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors that preserve symmetry presents a significant challenge. The ICT decomposition and a basis of this equivariant space are difficult to obtain for high-order tensors. After decades of research, we recently achieve an explicit ICT decomposition for $n=5$ \citep{bonvicini2024irreducible} with factorial time/space complexity. This work, for the first time, obtains decomposition matrices for ICTs up to rank $n=9$ with reduced and affordable complexity, by constructing what we call path matrices. The path matrices are obtained via performing chain-like contraction with Clebsch-Gordan matrices following the parentage scheme. We prove and leverage that the concatenation of path matrices is an orthonormal change-of-basis matrix between the Cartesian tensor product space and the spherical direct sum spaces. Furthermore, we identify a complete orthogonal basis for the equivariant space, rather than a spanning set \citep{pearce2023brauer}, through this path matrices technique. We further extend our result to the arbitrary tensor product and direct sum spaces, enabling free design between different spaces while keeping symmetry. The Python code is available in the appendix where the $n=6,\dots,9$ ICT decomposition matrices are obtained in <0.1s, 0.5s, 1s, 3s, 11s, and 4m32s, respectively.

arXiv:2412.18406v1 Announce Type: cross Abstract: Mechanobiology is gaining more and more traction as the fundamental role of physical forces in biological function becomes clearer. Forces at the microscale are often measured indirectly using inverse problems such as Traction Force Microscopy because biological experiments are hard to access with physical probes. In contrast with the experimental nature of biology and physics, these measurements do not come with error bars, confidence regions, or p-values. The aim of this manuscript is to publicize this issue and to propose a first step towards a remedy in the form of a general reconstruction framework that enables hypothesis testing.

arXiv:2407.12527v2 Announce Type: replace-cross Abstract: The Discrete Ordinates Method (DOM) is the most widely used velocity discretiza-tion method for simulating the radiative transport equation. However, the ray effect is a long-standing drawback of DOM. In benchmark tests that exhibit the ray effect, we observe low regularity in the velocity variable of the solution. To address this issue, we propose a Random Ordinate Method (ROM) to mitigate the ray effect. Compared to other strategies proposed in the literature for mitigating the ray effect, ROM offers several advantages: 1) the computational cost is comparable to that of DOM; 2) it is simple and requires minimal changes to existing DOM-based code; 3) it is easily parallelizable and independent of the problem setup. A formal analysis is presented for the convergence orders of the error and bias. Numerical tests demonstrate the reduction in computational cost compared toDOM, as well as its effectiveness in mitigating the ray effect.

arXiv:2412.17908v1 Announce Type: new Abstract: With the rapid development of generative artificial intelligence, particularly large language models, a number of sub-fields of deep learning have made significant progress and are now very useful in everyday applications. For example, well-known financial institutions simulate a wide range of scenarios for various models created by their research teams using reinforcement learning, both before production and after regular operations. In this work, we propose a backdoor attack that focuses solely on data poisoning. This particular backdoor attack is classified as an attack without prior consideration or trigger, and we name it FinanceLLMsBackRL. Our aim is to examine the potential effects of large language models that use reinforcement learning systems for text production or speech recognition, finance, physics, or the ecosystem of contemporary artificial intelligence models.

arXiv:2411.15722v2 Announce Type: replace Abstract: We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion batteries. We establish optimal-order error estimates for the solution in the norms $l^2(H^1)$ and $l^2(L^2(H^q_r))$, $q=0,1$. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers.

arXiv:2412.16787v1 Announce Type: new Abstract: Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose, but neural network-based methods that incorporate these principles remain underexplored. This work introduces SympFlow, a time-dependent symplectic neural network designed using parameterized Hamiltonian flow maps. This design allows for backward error analysis and ensures the preservation of the symplectic structure. SympFlow allows for two key applications: (i) providing a time-continuous symplectic approximation of the exact flow of a Hamiltonian system--purely based on the differential equations it satisfies, and (ii) approximating the flow map of an unknown Hamiltonian system relying on trajectory data. We demonstrate the effectiveness of SympFlow on diverse problems, including chaotic and dissipative systems, showing improved energy conservation compared to general-purpose numerical methods and accurate

arXiv:2412.16845v1 Announce Type: new Abstract: In this paper, we present a gas-kinetic scheme using discrete velocity space to solve Maxwell equations. The kinetic model recovers Maxwell equations in the zero relaxation time limit. The scheme achieves second-order spatial and temporal accuracy in structured meshes comparable to the finite-difference time-domain (FDTD) method, without requiring staggered grids or leapfrog discretization. Our kinetic scheme is inherently multidimensional due to its use of kinetic beams in multiple directions, allowing larger time steps in multidimensional computations. It demonstrates better stability than FDTD when handling discontinuities and readily extends to unstructured meshes. We validate the method through various test cases including antenna simulation, sphere scattering, and flight vehicle scattering. The results align well with Riemann-solver-based solutions. Finally, we examine charge conservation for Maxwell equations through test cases.

arXiv:2412.17369v1 Announce Type: new Abstract: We propose in this work a second-order Langevin sampler for the isothermal-isobaric ensemble (the NPT ensemble), preserving a positive volume for the simulation box. We first derive the suitable equations of motion for particles to be coupled with the overdamped Langevin equation of volume by sending the artificial mass of the periodic box to zero in the work of Liang et. al. [J. Chem. Phys. 157(14)]. We prove the well-posedness of the new system of equations and show that its invariant measure is the desired ensemble. The new continuous time equations not only justify the previous cell-rescaling methods, but also allow us to choose a suitable friction coefficient so that one has additive noise after a change of variable by taking logarithm of the volume. This observation allows us to propose a second order weak scheme that guarantees the positivity of the volume. Various numerical experiments have been performed to demonstrate the efficacy of our method.

arXiv:2412.17571v1 Announce Type: new Abstract: This paper presents the innovative HPCNeuroNet model, a pioneering fusion of Spiking Neural Networks (SNNs), Transformers, and high-performance computing tailored for particle physics, particularly in particle identification from detector responses. Our approach leverages SNNs' intrinsic temporal dynamics and Transformers' robust attention mechanisms to enhance performance when discerning intricate particle interactions. At the heart of HPCNeuroNet lies the integration of the sequential dynamism inherent in SNNs with the context-aware attention capabilities of Transformers, enabling the model to precisely decode and interpret complex detector data. HPCNeuroNet is realized through the HLS4ML framework and optimized for deployment in FPGA environments. The model accuracy and scalability are also enhanced by this architectural choice. Benchmarked against machine learning models, HPCNeuroNet showcases better performance metrics, underlining its transformative potential in high-energy physics. We demonstrate that the combination of SNNs, Transformers, and FPGA-based high-performance computing in particle physics signifies a significant step forward and provides a strong foundation for future research.

arXiv:2412.16644v1 Announce Type: cross Abstract: Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is often computationally expensive and time-consuming. An alternative approach involves transforming PDEs into integral equations and solving them using Green's functions, which provide analytical solutions. Nevertheless, deriving Green's functions analytically is a challenging and non-trivial task, particularly for complex systems. In this study, we introduce a novel framework, termed GreensONet, which is constructed based on the strucutre of deep operator networks (DeepONet) to learn embedded Green's functions and solve PDEs via Green's integral formulation. Specifically, the Trunk Net within GreensONet is designed to approximate the unknown Green's functions of the system, while the Branch Net are utilized to approximate the auxiliary gradients of the Green's function. These outputs are subsequently employed to perform surface integrals and volume integrals, incorporating user-defined boundary conditions and source terms, respectively. The effectiveness of the proposed framework is demonstrated on three types of PDEs in bounded domains: 3D heat conduction equations, reaction-diffusion equations, and Stokes equations. Comparative results in these cases demonstrate that GreenONet's accuracy and generalization ability surpass those of existing methods, including Physics-Informed Neural Networks (PINN), DeepONet, Physics-Informed DeepONet (PI-DeepONet), and Fourier Neural Operators (FNO).

arXiv:2410.21824v2 Announce Type: replace Abstract: Data privacy is a significant concern when using numerical simulations for sensitive information such as medical, financial, or engineering data. This issue becomes especially relevant in untrusted environments like public cloud infrastructures. Fully homomorphic encryption (FHE) offers a promising solution for achieving data privacy by enabling secure computations directly on encrypted data. In this paper, aimed at computational scientists, we explore the viability of FHE-based, privacy-preserving numerical simulations of partial differential equations. We begin with an overview of the CKKS scheme, a widely used FHE method for computations with real numbers. Next, we introduce our Julia-based packages OpenFHE$.$jl and SecureArithmetic$.$jl, which wrap the OpenFHE C++ library and provide a convenient interface for secure arithmetic operations. We then evaluate the accuracy and performance of key FHE operations in OpenFHE as a baseline for more complex numerical algorithms. Following that, we demonstrate the application of FHE to scientific computing by implementing two finite difference schemes for the linear advection equation. Finally, we discuss potential challenges and solutions for extending secure numerical simulations to other models and methods. Our results show that cryptographically secure numerical simulations are possible, but that careful consideration must be given to the computational overhead and the numerical errors introduced by using FHE.

arXiv:2412.16234v1 Announce Type: new Abstract: We uncover a phenomenon largely overlooked by the scientific community utilizing AI: neural networks exhibit high susceptibility to minute perturbations, resulting in significant deviations in their outputs. Through an analysis of five diverse application areas -- weather forecasting, chemical energy and force calculations, fluid dynamics, quantum chromodynamics, and wireless communication -- we demonstrate that this vulnerability is a broad and general characteristic of AI systems. This revelation exposes a hidden risk in relying on neural networks for essential scientific computations, calling further studies on their reliability and security.