arXiv subjects

William Anderson

Publications and source records attributed to William Anderson.

At least 19 recordsLinked to original sources

arXiv2026

Physics-Informed Latent Space Dynamics Identification for Time-Dependent NLTE Atomic Kinetics

Non-local thermodynamic equilibrium (NLTE) calculations remain a major computational bottleneck in radiation--hydrodynamics, while most existing machine-learning surrogates treat NLTE as a static input--output mapping rather than a kinetic evolution problem. Here, we present a physics-informed Latent Space Dynamics Identification (pLaSDI) framework specifically designed for NLTE atomic kinetics, which captures the time-dependent atomic kinetics of non-equilibrium plasmas through an explicit reduced governing equation. To ensure the physical reliability of the reduced model, we impose physics-informed loss terms that enforce macroscopic consistency, dynamical stability, and convergence to the correct steady state during long-time integration. Applied to tin NLTE population data generated along hydrodynamically modeled temperature--density trajectories relevant to extreme ultraviolet (EUV) lithography plasmas, the model accurately reproduces charge-state evolution and mean charge state with errors below 2\%, achieves speedups of approximately $5\times10^{4}$--$10^{5}$, and remains stable outside the training trajectories by converging toward physically admissible states and the correct steady-state solution under fixed plasma conditions. These results show that careful physics-informed design of the latent dynamics, rather than data fitting alone, is essential for constructing fast, stable, and physically reliable extrapolative surrogates for time-dependent NLTE kinetics.

physics.plasm-ph↗

arXiv2025

Sequential decoder training for improved latent space dynamics identification

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

cs.LG↗

arXiv2025

mLaSDI: Multi-stage latent space dynamics identification

Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs). Recently, Latent Space Dynamics Identification (LaSDI) was proposed as a data-driven, non-intrusive ROM framework. LaSDI compresses the training data via an autoencoder and learns user-specified ordinary differential equations (ODEs), governing the latent dynamics, enabling rapid predictions for unseen parameters. While LaSDI has produced effective ROMs for numerous problems, the autoencoder must simultaneously reconstruct the training data and satisfy the imposed latent dynamics, which are often competing objectives that limit accuracy, particularly for complex or high-frequency phenomena. To address this limitation, we propose multi-stage Latent Space Dynamics Identification (mLaSDI). With mLaSDI, we train LaSDI sequentially in stages. After training the initial autoencoder, we train additional decoders which map the latent trajectories to residuals from previous stages. This staged residual learning, combined with periodic activation functions, enables recovery of high-frequency content without sacrificing interpretability of the latent dynamics. We further provide an error decomposition separating autoencoder and latent dynamics contributions, and prove that additional training stages cannot increase the training residual. Numerical experiments on a multiscale oscillating system, unsteady wake flow, and the 1D-1V Vlasov equation demonstrate that mLaSDI achieves significantly lower reconstruction and prediction errors, often by an order of magnitude, while requiring less training time and reduced hyperparameter tuning compared to standard LaSDI.

cs.LG↗

arXiv2025

Defining Foundation Models for Computational Science: A Call for Clarity and Rigor

The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that as the term "foundation model" is an evolving concept, its application in computational science is increasingly used without a universally accepted definition, potentially creating confusion and diluting its precise scientific meaning. In this paper, we address this gap by proposing a formal definition of foundation models in computational science, grounded in the core values of generality, reusability, and scalability. We articulate a set of essential and desirable characteristics that such models must exhibit, drawing parallels with traditional foundational methods, like the finite element and finite volume methods. Furthermore, we introduce the Data-Driven Finite Element Method (DD-FEM), a framework that fuses the modular structure of classical FEM with the representational power of data-driven learning. We demonstrate how DD-FEM addresses many of the key challenges in realizing foundation models for computational science, including scalability, adaptability, and physics consistency. By bridging traditional numerical methods with modern AI paradigms, this work provides a rigorous foundation for evaluating and developing novel approaches toward future foundation models in computational science.

cs.LG↗

arXiv2024

Identifying feedback directions in the mechanisms driving self-sustained thermoacoustic instability in a single-element rocket combustor

The occurrence of high frequency (>1000 Hz) thermoacoustic instability (TAI) sustained by mutual feedback among the acoustic field, heat release rate oscillations, and hydrodynamic oscillations poses severe challenges to the operation and structural integrity of rocket engines. Hence, quantifying the differing levels of feedback between these variables can help uncover the underlying mechanisms behind such high frequency TAI, enabling redesign of combustors to mitigate TAI. However, so far, no concrete method exists to decipher the varying levels of mutual feedback during high-frequency TAI. In the present study, we holistically investigate the mutual influence based on the spatiotemporal directionality among acoustic pressure, heat release rate, hydrodynamic and thermal oscillations during TAI of a single-element rocket engine combustor. Using symbolic transfer entropy (STE), we identify the spatiotemporal direction of feedback interactions between those primary variables when acoustic waves significantly emerge during TAI. We unveil the influence of vorticity dynamics at the fuel collar (or the propellant splitter plate) as the primary stimulant over the heat release rate fluctuations to rapidly amplify the amplitude of the acoustic field. Further, depending on the quantification of the degree of the mutual information (i.e., the net direction of information), we identify the switches in dominating the thermoacoustic driving between the variables during TAI, each representing a distinct mechanism of a thermoacoustic state. Additionally, from this quantification, we analyze the relative dominance of the variables and rank-order the mutual feedback according to their impact on driving TAI.

physics.flu-dyn↗

arXiv2024

Computational Fluid Dynamics: its Carbon Footprint and Role in Carbon Emission Reduction

Turbulent flow physics regulates the aerodynamic properties of lifting surfaces, the thermodynamic efficiency of vapor power systems, and exchanges of natural and anthropogenic quantities between the atmosphere and ocean, to name just a few applications. The dynamics of turbulent flows are described via numerical integration of the non-linear Navier-Stokes equation -- a procedure known as computational fluid dynamics (CFD). At the dawn of scientific computing in the late 1950s, it would be many decades before terms such as ``carbon footprint'' or ``sustainability'' entered the lexicon, and longer still before these themes attained national priority throughout advanced economies. This paper introduces a framework designed to calculate the carbon footprint of CFD and its contribution to carbon emission reduction strategies. We will distinguish between "hero" and "routine" calculations, noting that the carbon footprint of hero calculations is largely determined by the energy source mix utilized. We will also review CFD of flows where turbulence effects are modeled, thus reducing the degrees of freedom. Estimates of the carbon footprint are presented for such fully- and partially-resolved simulations as functions of turbulence activity and calculation year, demonstrating a reduction in carbon emissions by two to five orders of magnitude at practical conditions. Beyond analyzing CO2 emissions, we quantify the benefits of applying CFD towards overall carbon emission reduction. The community's effort to avoid redundant calculations via turbulence databases merits particular attention, with estimates indicating that a single database could potentially reduce CO2 emissions by approximately O(1) million metric tons. Additionally, implementing CFD in the fluids industry has markedly decreased dependence on wind tunnel testing, which is anticipated to lead to CO2 emission reduction.

physics.soc-ph↗

arXiv2024

Eclectic Rule Extraction for Explainability of Deep Neural Network based Intrusion Detection Systems

This paper addresses trust issues created from the ubiquity of black box algorithms and surrogate explainers in Explainable Intrusion Detection Systems (X-IDS). While Explainable Artificial Intelligence (XAI) aims to enhance transparency, black box surrogate explainers, such as Local Interpretable Model-Agnostic Explanation (LIME) and SHapley Additive exPlanation (SHAP), are difficult to trust. The black box nature of these surrogate explainers makes the process behind explanation generation opaque and difficult to understand. To avoid this problem, one can use transparent white box algorithms such as Rule Extraction (RE). There are three types of RE algorithms: pedagogical, decompositional, and eclectic. Pedagogical methods offer fast but untrustworthy white-box explanations, while decompositional RE provides trustworthy explanations with poor scalability. This work explores eclectic rule extraction, which strikes a balance between scalability and trustworthiness. By combining techniques from pedagogical and decompositional approaches, eclectic rule extraction leverages the advantages of both, while mitigating some of their drawbacks. The proposed Hybrid X-IDS architecture features eclectic RE as a white box surrogate explainer for black box Deep Neural Networks (DNN). The presented eclectic RE algorithm extracts human-readable rules from hidden layers, facilitating explainable and trustworthy rulesets. Evaluations on UNSW-NB15 and CIC-IDS-2017 datasets demonstrate the algorithm's ability to generate rulesets with 99.9% accuracy, mimicking DNN outputs. The contributions of this work include the hybrid X-IDS architecture, the eclectic rule extraction algorithm applicable to intrusion detection datasets, and a thorough analysis of performance and explainability, demonstrating the trade-offs involved in rule extraction speed and accuracy.

cs.CR↗

arXiv2023

Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions

The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this partial differential equation (PDE) using conventional numerical methods becomes computationally prohibitive. Here, we introduce a fast, scalable, and interpretable method for solving the Fokker-Planck equation which is applicable in higher dimensions. This method approximates the solution as a linear combination of shape-morphing Gaussians with time-dependent means and covariances. These parameters evolve according to the method of reduced-order nonlinear solutions (RONS) which ensures that the approximate solution stays close to the true solution of the PDE for all times. As such, the proposed method approximates the transient dynamics as well as the equilibrium density, when the latter exists. Our approximate solutions can be viewed as an evolution on a finite-dimensional statistical manifold embedded in the space of probability densities. We show that the metric tensor in RONS coincides with the Fisher information matrix on this manifold. We also discuss the interpretation of our method as a shallow neural network with Gaussian activation functions and time-varying parameters. In contrast to existing deep learning methods, our method is interpretable, requires no training, and automatically ensures that the approximate solution satisfies all properties of a probability density.

math.DS↗

arXiv2023

REGARD: Rules of EngaGement for Automated cybeR Defense to aid in Intrusion Response

Automated Intelligent Cyberdefense Agents (AICAs) that are part Intrusion Detection Systems (IDS) and part Intrusion Response Systems (IRS) are being designed to protect against sophisticated and automated cyber-attacks. An AICA based on the ideas of Self-Adaptive Autonomic Computing Systems (SA-ACS) can be considered as a managing system that protects a managed system like a personal computer, web application, critical infrastructure, etc. An AICA, specifically the IRS components, can compute a wide range of potential responses to meet its security goals and objectives, such as taking actions to prevent the attack from completing, restoring the system to comply with the organizational security policy, containing or confining an attack, attack eradication, deploying forensics measures to enable future attack analysis, counterattack, and so on. To restrict its activities in order to minimize collateral/organizational damage, such an automated system must have set Rules of Engagement (RoE). Automated systems must determine which operations can be completely automated (and when), which actions require human operator confirmation, and which actions must never be undertaken. In this paper, to enable this control functionality over an IRS, we create Rules of EngaGement for Automated cybeR Defense (REGARD) system which holds a set of Rules of Engagement (RoE) to protect the managed system according to the instructions provided by the human operator. These rules help limit the action of the IRS on the managed system in compliance with the recommendations of the domain expert. We provide details of execution, management, operation, and conflict resolution for Rules of Engagement (RoE) to constrain the actions of an automated IRS. We also describe REGARD system implementation, security case studies for cyber defense, and RoE demonstrations.

cs.CR↗

arXiv2023

Explainable Intrusion Detection Systems Using Competitive Learning Techniques

The current state of the art systems in Artificial Intelligence (AI) enabled intrusion detection use a variety of black box methods. These black box methods are generally trained using Error Based Learning (EBL) techniques with a focus on creating accurate models. These models have high performative costs and are not easily explainable. A white box Competitive Learning (CL) based eXplainable Intrusion Detection System (X-IDS) offers a potential solution to these problem. CL models utilize an entirely different learning paradigm than EBL approaches. This different learning process makes the CL family of algorithms innately explainable and less resource intensive. In this paper, we create an X-IDS architecture that is based on DARPA's recommendation for explainable systems. In our architecture we leverage CL algorithms like, Self Organizing Maps (SOM), Growing Self Organizing Maps (GSOM), and Growing Hierarchical Self Organizing Map (GHSOM). The resulting models can be data-mined to create statistical and visual explanations. Our architecture is tested using NSL-KDD and CIC-IDS-2017 benchmark datasets, and produces accuracies that are 1% - 3% less than EBL models. However, CL models are much more explainable than EBL models. Additionally, we use a pruning process that is able to significantly reduce the size of these CL based models. By pruning our models, we are able to increase prediction speeds. Lastly, we analyze the statistical and visual explanations generated by our architecture, and we give a strategy that users could use to help navigate the set of explanations. These explanations will help users build trust with an Intrusion Detection System (IDS), and allow users to discover ways to increase the IDS's potency.

cs.CR↗

arXiv2022

Designing an Artificial Immune System inspired Intrusion Detection System

The Human Immune System (HIS) works to protect a body from infection, illness, and disease. This system can inspire cybersecurity professionals to design an Artificial Immune System (AIS) based Intrusion Detection System (IDS). These biologically inspired algorithms using Self/Nonself and Danger Theory can directly augmentIDS designs and implementations. In this paper, we include an examination into the elements of design necessary for building an AIS-IDS framework and present an architecture to create such systems.

cs.CR↗

arXiv2022

Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks

We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent partial differential equations (PDEs), where the modes depend nonlinearly on a set of time-varying parameters. RONS uses a set of ordinary differential equations (ODEs) for the parameters to optimally evolve the shape of the modes to adapt to the PDE's solution. This method has already proven extremely effective in tackling challenging problems such as advection-dominated flows and high-dimensional PDEs. However, as the number of parameters grow, integrating the RONS equation and even its formation become computationally prohibitive. Here, we develop three separate methods to address these computational bottlenecks: symbolic RONS, collocation RONS and regularized RONS. We demonstrate the efficacy of these methods on two examples: Fokker-Planck equation in high dimensions and the Kuramoto-Sivashinsky equation. In both cases, we observe that the proposed methods lead to several orders of magnitude in speedup and accuracy. Our proposed methods extend the applicability of RONS beyond reduced-order modeling by making it possible to use RONS for accurate numerical solution of linear and nonlinear PDEs. Finally, as a special case of RONS, we discuss its application to problems where the PDE's solution is approximated by a neural network, with the time-dependent parameters being the weights and biases of the network. The RONS equations dictate the optimal evolution of the network's parameters without requiring any training.

math.DS↗

arXiv2022

Creating an Explainable Intrusion Detection System Using Self Organizing Maps

Modern Artificial Intelligence (AI) enabled Intrusion Detection Systems (IDS) are complex black boxes. This means that a security analyst will have little to no explanation or clarification on why an IDS model made a particular prediction. A potential solution to this problem is to research and develop Explainable Intrusion Detection Systems (X-IDS) based on current capabilities in Explainable Artificial Intelligence (XAI). In this paper, we create a Self Organizing Maps (SOMs) based X-IDS system that is capable of producing explanatory visualizations. We leverage SOM's explainability to create both global and local explanations. An analyst can use global explanations to get a general idea of how a particular IDS model computes predictions. Local explanations are generated for individual datapoints to explain why a certain prediction value was computed. Furthermore, our SOM based X-IDS was evaluated on both explanation generation and traditional accuracy tests using the NSL-KDD and the CIC-IDS-2017 datasets.

cs.CR↗

arXiv2022

Explainable Intrusion Detection Systems (X-IDS): A Survey of Current Methods, Challenges, and Opportunities

The application of Artificial Intelligence (AI) and Machine Learning (ML) to cybersecurity challenges has gained traction in industry and academia, partially as a result of widespread malware attacks on critical systems such as cloud infrastructures and government institutions. Intrusion Detection Systems (IDS), using some forms of AI, have received widespread adoption due to their ability to handle vast amounts of data with a high prediction accuracy. These systems are hosted in the organizational Cyber Security Operation Center (CSoC) as a defense tool to monitor and detect malicious network flow that would otherwise impact the Confidentiality, Integrity, and Availability (CIA). CSoC analysts rely on these systems to make decisions about the detected threats. However, IDSs designed using Deep Learning (DL) techniques are often treated as black box models and do not provide a justification for their predictions. This creates a barrier for CSoC analysts, as they are unable to improve their decisions based on the model's predictions. One solution to this problem is to design explainable IDS (X-IDS). This survey reviews the state-of-the-art in explainable AI (XAI) for IDS, its current challenges, and discusses how these challenges span to the design of an X-IDS. In particular, we discuss black box and white box approaches comprehensively. We also present the tradeoff between these approaches in terms of their performance and ability to produce explanations. Furthermore, we propose a generic architecture that considers human-in-the-loop which can be used as a guideline when designing an X-IDS. Research recommendations are given from three critical viewpoints: the need to define explainability for IDS, the need to create explanations tailored to various stakeholders, and the need to design metrics to evaluate explanations.

cs.CR↗

arXiv2022

The Western Australian Optical Ground Station

Free-space communications at optical wavelengths offers the potential for orders-of-magnitude improvement in data rates over conventional radio wavelengths, and this will be needed to meet the demand of future space-to-ground applications. Supporting this new paradigm necessitates a global network of optical ground stations. This paper describes the architecture and commissioning of the Western Australian Optical Ground Station, to be installed on the roof of the physics building at the University of Western Australia. This ground station will incorporate amplitude- and phase-stabilisation technology, previously demonstrated over horizontal free-space links, into the ground station's optical telescope. Trialling this advanced amplitude- and phase-stabilisation technology, the ground station will overcome turbulence-induced noise to establish stable, coherent free-space links between ground-to-air and ground-to-space. These links will enable significant advances in high-speed and quantum-secured communications; positioning, navigation, and timing; and fundamental physics.

physics.ins-det↗

arXiv2022

Shape-morphing reduced-order models for nonlinear Schrodinger equations

We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational formulation of NLS and (ii) The recently developed method of reduced-order nonlinear solutions (RONS). First, we prove the surprising result that, although the two methods are seemingly quite different, they can be obtained from the real and imaginary parts of a single complex-valued master equation. Furthermore, for the NLS equation in a stationary frame, we show that the reduced Lagrangian method fails to predict the correct group velocity of the waves whereas RONS predicts the correct group velocity. Finally, for the modified NLS equation, where the reduced Lagrangian approach is inapplicable, the RONS reduced-order model accurately approximates the true solutions.

math.DS↗

arXiv2021

Coupled interaction between acoustics and unsteady flame dynamics during the transition to thermoacoustic instability in a multi-element rocket combustor

Rocket engine combustors are prone to transverse instabilities that are characterized by large amplitude high frequency oscillations in the acoustic pressure and the heat release rate. We study the coupled interaction between the acoustic pressure and the CH* intensity oscillations in a 2D multi-element self-excited model rocket combustor during the transition from a stable state to thermoacoustic instability through intermittency. We show the emergence of synchronization between these oscillations from desynchronization through intermittent phase synchronization during the onset of thermoacoustic instability. We find substantial evidence that the intensities of the jet flames close to the end wall is higher than that observed near the center of the combustor as a result of its strong coupling to the local acoustic field. Using concepts from recurrence theory, we distinguish the type of synchronization between the acoustic pressure and the CH* intensity oscillations at the end wall and the center of the combustor during thermoacoustic instability. Analyzing the local CH* intensity oscillations, we observe that the longitudinally propagating jet flames experience substantial transverse displacement with flame merging effects during thermoacoustic instability. Furthermore, we differentiate the interaction of the jet flames with the shock wave during intermittency and thermoacoustic instability at both the end wall and the center of the combustor. We also discerned the change from stochastic to deterministic nature in the local CH* intensity oscillations during the transition to thermoacoustic instability. Our results demonstrate that only the first few transverse modes contribute to the generation of acoustic power from the reacting flow, in spite of the pressure oscillations featuring several harmonics.

physics.flu-dyn↗

arXiv2021

Using Uncertainty in Deep Learning Reconstruction for Cone-Beam CT of the Brain

Contrast resolution beyond the limits of conventional cone-beam CT (CBCT) systems is essential to high-quality imaging of the brain. We present a deep learning reconstruction method (dubbed DL-Recon) that integrates physically principled reconstruction models with DL-based image synthesis based on the statistical uncertainty in the synthesis image. A synthesis network was developed to generate a synthesized CBCT image (DL-Synthesis) from an uncorrected filtered back-projection (FBP) image. To improve generalizability (including accurate representation of lesions not seen in training), voxel-wise epistemic uncertainty of DL-Synthesis was computed using a Bayesian inference technique (Monte-Carlo dropout). In regions of high uncertainty, the DL-Recon method incorporates information from a physics-based reconstruction model and artifact-corrected projection data. Two forms of the DL-Recon method are proposed: (i) image-domain fusion of DL-Synthesis and FBP (DL-FBP) weighted by DL uncertainty; and (ii) a model-based iterative image reconstruction (MBIR) optimization using DL-Synthesis to compute a spatially varying regularization term based on DL uncertainty (DL-MBIR). The error in DL-Synthesis images was correlated with the uncertainty in the synthesis estimate. Compared to FBP and PWLS, the DL-Recon methods (both DL-FBP and DL-MBIR) showed ~50% reduction in noise (at matched spatial resolution) and ~40-70% improvement in image uniformity. Conventional DL-Synthesis alone exhibited ~10-60% under-estimation of lesion contrast and ~5-40% reduction in lesion segmentation accuracy (Dice coefficient) in simulated and real brain lesions, suggesting a lack of reliability / generalizability for structures unseen in the training data. DL-FBP and DL-MBIR improved the accuracy of reconstruction by directly incorporating information from the measurements in regions of high uncertainty.

physics.med-ph↗