arXiv subjects

Krishna Garikipati

Publications and source records attributed to Krishna Garikipati.

At least 19 recordsLinked to original sources

arXiv2026

Resource Analysis for Quantum Simulation of Spatially Varying Transport-Reaction Equations

Spatially varying coefficients are the primary source of circuit complexity in quantum simulation of linear advection-diffusion-reaction equations. This work presents a resource analysis of single-step quantum propagators constructed using sparse FABLE block encodings, Quantum Singular Value Transformation, and linear-combination-of-unitaries. We derive theoretical estimates for qubit count, gate complexity, and circuit depth in terms of the spatial discretization, sparsity, and polynomial degree, and compare these predictions with synthesized quantum circuits for one- and two-dimensional variable-coefficient problems. The resulting analysis quantifies the cost of encoding realistic transport operators and provides practical resource estimates for near-term implementations.

quant-ph↗

arXiv2026

Materials Behavior as Mechanism Ensembles: A Probabilistic Framework for Emergent Behaviors

Materials behavior is often treated as a deterministic mapping from structure to properties, yet many important phenomena emerge from the conditional activation of multiple mechanisms across scales. This is especially evident in fatigue of metals, where crack growth is typically modeled as monotonic and irreversible process, despite evidence that local microstructure, loading history, and competing unit processes can shift the balance among propagation, arrest, and self-healing. Here we present a probabilistic framework that describes materials behavior as an ensemble of constituent mechanisms whose activation, interaction, and evolution determine emergent outcomes. The framework connects mechanism activation, state evolution, and macroscopic observables in a probabilistic way. In the case of fatigue crack propagation, it reframes damage tolerance as an inference problem over mechanism competition and provides a basis for integrating multiscale simulation, multimodal characterization, and machine learning. The same logic extends to other physical and chemical systems suggesting a portable framework for any system in which emergent behavior reflects mechanism competition under changing conditions. The broader ambition of this perspective review is a shift from correlating structure and performance after the fact to identifying, in advance, the conditions that make desired emergent behavior probable.

cond-mat.mtrl-sci↗

arXiv2026

Learning Population-Level Dynamics through a Latent Fokker--Planck Model and Discrepancy Transport Maps

Many scientific and engineering systems are observed as time-indexed probability distributions whose governing dynamics are unknown and whose individual trajectories are unavailable. These settings challenge conventional system-identification approaches that rely on trajectory correspondence or prescribed evolution equations. This work presents a population-level inference framework that recovers latent stochastic dynamics directly from snapshot probability distributions by decomposing the observed evolution into an intrinsic latent stochastic process and a discrepancy transport map that captures geometric deformation between the latent and observed probability spaces. The latent dynamics are modeled using an Ornstein--Uhlenbeck process, providing a closed-form solution to the associated Fokker--Planck equation, while the discrepancy transport map is parameterized through the Knothe--Rosenblatt rearrangement with monotone neural networks. To mitigate the non-uniqueness inherent in the latent--transport decomposition, the transport map is regularized using a deformation energy motivated by hyperelasticity, promoting smooth, physically interpretable deformations while reducing unnecessary complexity. The latent stochastic model and discrepancy transport map are learned jointly through a unified optimization problem defined over probability distributions. Numerical examples involving nonlinear and multimodal distributional dynamics demonstrate that the proposed framework accurately reconstructs complex probability evolution while preserving a compact and analytically tractable latent representation. The proposed formulation provides a general framework for population-level dynamical inference and establishes a foundation for extending latent stochastic models and transport-based learning to more general and higher-dimensional systems.

cs.CE↗

arXiv2026

Bayesian Variational System Identification with Weak-Form Residual Likelihoods

We consider system identification for discovering parameterized operators in governing partial differential equations (PDEs) from noisy spatiotemporal data. Building on variational system identification (VSI), which identifies PDEs through Galerkin weak-form residuals, we develop a Bayesian VSI (B-VSI) framework for operator selection, parameter estimation, and uncertainty quantification. The central idea is to define the likelihood directly in weak-form residual space by propagating observation uncertainty through the weak-form residual map. The resulting likelihood captures heteroscedastic and correlated residual errors while avoiding repeated forward PDE solves during inference. For efficient computation, we use lagged-covariance updates that yield generalized least-squares estimates and conjugate posterior approximations when applicable, together with gradient-based and particle-based methods for more general priors and posterior structures. Model-form uncertainty is handled through sequential operator elimination guided by a residual-space Bayesian information criterion. We demonstrate the framework on state-linear and nonlinear PDEs, including the Fokker--Planck equation and a two-field Cahn--Hilliard equation. The results show that B-VSI accurately recovers active operators and coefficients from noisy data, improves robustness relative to classical VSI, and provides posterior uncertainty estimates for coefficients and derived physical quantities.

cs.CE↗

arXiv2026

Constitutive parameter inference using physics-based data-driven modeling in full volume datasets of intact and torn rotator cuff tendons

In this work, we characterized the material properties of an animal model of the rotator cuff tendon using full volume datasets of both its intact and injured states by capturing internal strain behavior throughout the tendon. Our experimental setup, involving tension along the fiber direction, activated volumetric, tensile, and shear mechanisms due to the tendon's complex geometry. We implemented an approach to model inference that we refer to as variational system identification (VSI) to solve the weak form of the stress equilibrium equation using these full volume displacements. Three constitutive models were used for parameter inference: a neo-Hookean model, a modified Holzapfel-Gasser-Ogden (HGO) model with higher-order terms in the first and second invariants, and a reduced polynomial model consisting of terms based on the first, second, and fiber-related invariants. Inferred parameters were further refined using an adjoint-based partial differential equation (PDE)-constrained optimization framework. Our results show that the modified HGO model captures the tendon's deformation mechanisms with reasonable accuracy, while the neo-Hookean model fails to reproduce key internal features, particularly the shear behavior in the injured tendon. Surprisingly, the simplified polynomial model performed comparably to the modified HGO formulation using only three terms. These findings suggest that while current constitutive models do not fully replicate the complex internal mechanics of the tendon, they are capable of capturing key trends in both intact and damaged tissue, using a homogeneous modeling approach. Continued model development is needed to bridge this gap and enable clinical-grade, predictive simulations of tendon injury and repair.

physics.bio-ph↗

arXiv2025

Assessing Coronary Microvascular Dysfunction using Angiography-based Data-driven Methods

Coronary microvascular dysfunction (CMD), characterized by impaired regulation of blood flow in the coronary microcirculation, plays a key role in the pathogenesis of ischemic heart disease and is increasingly recognized as a contributor to adverse cardiovascular outcomes. Despite its clinical importance, CMD remains underdiagnosed due to the reliance on invasive procedures such as pressure wire-based measurements of the index of microcirculatory resistance (IMR) and coronary flow reserve (CFR), which are costly, time-consuming, and carry procedural risks. To date, no study has sought to quantify CMD indices using data-driven approaches while leveraging the rich information contained in coronary angiograms. To address these limitations, this study proposes a novel data-driven framework for inference of CMD indices based on coronary angiography. A physiologically validated multi-physics model was used to generate synthetic datasets for data-driven model training, consisting of CMD indices and computational angiograms with corresponding contrast intensity profiles (CIPs). Two neural network architectures were developed: a single-input-channel encoder-MLP model for IMR prediction and a dual-input-channel encoder-MLP model for CFR prediction, both incorporating epistemic uncertainty estimation to quantify prediction confidence. Results demonstrate that the data-driven models achieve high predictive accuracy when evaluated against physics-based synthetic datasets, and that the uncertainty estimates are positively correlated with prediction errors. Furthermore, the utility of CIPs as informative surrogates for coronary physiology is demonstrated, underscoring the potential of the proposed framework to enable accurate, real-time, image-based CMD assessment using routine angiography without the need for more invasive approaches.

cs.CE↗

arXiv2025

The inference of Fokker-Planck equations via transport maps

We present a framework, which, from the trajectories detailing the spatiotemporal dynamics of a population, simultaneously reconstructs a transport map as well as the Fokker-Planck equation governing the coarse-grained probability distribution. Leveraging the Knothe-Rosenblatt rearrangement, we model the transport map from a fixed reference distribution to the target distribution, and derive the velocity fields of the flows from the trajectory of transport maps. Exploiting the velocity fields, we circumvent spatial gradients to infer the Fokker-Planck equation's potential and diffusivity. The sparsity of trajectories injects uncertainty, which we treat in a Bayesian setting using variational inference. The approach is applied to inferring the Fokker-Planck dynamics in spaces of up to five dimensions, demonstrating both accurate identification of the system and efficiency with respect to data size.

math.DS↗

arXiv2025

Equivariant graph neural network surrogates for predicting the properties of relaxed atomic configurations

Density functional theory (DFT) calculations determine the relaxed atomic positions and lattice parameters that minimize the formation energy of a structure. We present an equivariant graph neural network (EGNN) model to predict the outcome of DFT calculations for structures of interest. Cluster expansions are a well established approach for representing the formation energies. However, traditional cluster expansions are limited in their ability to handle variations from a fixed lattice, including interstitial atoms, amorphous materials, and materials with multiple structures. EGNNs offer a more flexible framework that inherently respects the symmetry of the system without being reliant on a particular lattice. In this work, we present the mathematical framework and the results of training for lithium cobalt oxide (LCO) at various compositions of lithium and arrangements of the lithium atoms. Our results demonstrate that the EGNN can accurately predict quantities outside the training set including the largest atomic displacements, the strain tensor and energy, and the formation energy providing greater insight into the system being studied without the need for more DFT calculations.

cond-mat.mtrl-sci↗

arXiv2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties associated with the mathematical and numerical treatment of fracture. The introduction of the diffuse field helps with crack propagation dynamics, enabling phase-field approaches to model all phases of damage from crack initiation to propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, leads to an array of possible models. There exists a large body of studies of these models and their consequences for crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used to model damage, its degradation of elastic response, and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). In this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

cond-mat.mtrl-sci↗

arXiv2025

AI University: An LLM-Powered Learning Assistant for Engineering---A Finite Element Method Case Study

We introduce AI University (AI-U), a flexible framework for AI-driven course content delivery that adapts to a course's instructional style. AI-U combines a fine-tuned large language model (LLM) with retrieval-augmented generation (RAG) and a reasoning synthesis model to generate style-aligned responses from lecture videos, notes, and textbooks. Using a graduate-level finite-element-method (FEM) course as a case study, we present a pipeline to synthesize course-grounded training data, fine-tune an open-source LLM with Low-Rank Adaptation (LoRA), and apply RAG-based synthesis. Our evaluation---combining cosine similarity, LLM-based assessment, expert review, and user studies---shows improved alignment with course materials relative to the base model. We have also developed a prototype web application, available at https://my-ai-university.com, that enhances AI-generated responses with references to relevant sections of the course material and clickable links to time-stamped video lectures. Our expert model is found to be higher scoring by a quantitative measure on 86% of test cases. An LLM judge also preferred our expert model to its base model under both evaluation prompts. Human evaluation by advanced users showed a preference for our expert model approximately twice as often as for the base model. The FEM course instructor found our expert model to achieve better alignment with class-specific content than a recent closed-weight model when both were combined with the reasoning synthesis model. AI-U offers a practical approach to developing course-specific learning assistants using fine-tuned and retrieval-augmented LLMs. By presenting our framework in an FEM class---central to training PhD and master's students in engineering science---we offer a template with potential for extension across STEM fields.

cs.CY↗

arXiv2025

Physics- and data-driven Active Learning of neural network representations for free energy functions of materials from statistical mechanics

Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed Monte Carlo data. To optimize sampling in the high-dimensional Monte Carlo space, we present an Active Learning framework that integrates space-filling sampling, uncertainty-based sampling, and physics-informed sampling. Additionally, our approach includes methods such as hyperparameter tuning, dynamic sampling, and novelty enforcement. These strategies can be combined to reduce MSE,either globally or in targeted regions of interest,while minimizing the number of required data points. The framework introduced here is broadly applicable to Monte Carlo sampling of a range of materials systems.

physics.comp-ph↗

arXiv2024

A Multi-physics Model of Flow from Coronary Angiography: Insights to Microvascular Function

Coronary Microvascular Dysfunction (CMD) is characterized by impaired vasodilation and can lead to insufficient blood flow to the myocardium during stress or exertion, affecting millions of people globally. Despite their diagnostic value, invasive, wire-based diagnosis techniques of CMD, such as index of microcirculatory resistance (IMR) and coronary flow reserve (CFR), are underutilized due to their complexity and inconsistency. Coronary angiography, one of the most commonly used imaging modalities, offers valuable flow information that assists in diagnosing CMD. However, this information is not fully understood or utilized in current clinical practice. In this study, a 3D-0D coupled multi-physics computational fluid dynamics (CFD) model was developed and calibrated to simulate and study the process of contrast injection and washout during clinical angiography. A contrast intensity profile (CIP) was introduced to describe the dynamics of coronary angiography data. Additionally, sensitivity studies were conducted to evaluate the influence of various coronary lumped parameter model (LPM) parameters on the shapes of CIPs. The results demonstrate that the multi-physics model can be effectively calibrated to produce physiologically meaningful hemodynamic results. Sensitivity studies reveal that resistance has a greater impact on the rising and falling slopes of CIP than capacitance, with higher resistance amplifying this effect. The model and results are presented here. These results are potentially transformative, as they provide a tool for interpreting angiographic data and ultimately extracting information concerning coronary microcirculation.

cs.CE↗

arXiv2024

A continuum, computational study of morphogenesis in lithium intermetallic interfaces

The design of solid state batteries with lithium anodes is attracting attention for the prospect of high capacity and improved safety over liquid electrolyte systems. The nature of transport with lithium as the current carrier has as a consequence the accretion or stripping away of the anode with every charge-discharge cycle. While this poses challenges from the growth of protrusions (dendrites) to loss of contact, there lurks an opportunity: Morphogenesis at the anode-electrolyte interface layer can be studied, and may ultimately be controlled as a factor in solid state battery design. The accessible interface morphologies, the dynamic paths to them, and mechanisms to control them expand considerably if lithium alloys are introduced in the anode. The thermodynamics and kinetics of lithium intermetallics present principled approaches for morphogenic interface design. In this communication we adopt a computational approach to such an exploration. With phase field models that are parameterized by a combination of first principles atomistic calculations and experiments, we present phenomenological studies of two lithium intermetallics: Li-Mg and Li-Zn. An array of parametric investigations follows on the influence of kinetics, charge-discharge rate, cycling, transport mechanisms and grain structure. The emphasis across these computations is on the dynamic morphogenesis of the intermetallic interface. Specifically, the plating, segregation and smooth distribution of Li, Mg and Zn, the growth and disappearance of voids, evolution of solid electrolyte-anode contact area, and grain boundary structure are investigated. The computational platform is a framework for future studies of morphogenic electrolyte-anode interfaces with more extensive inputs from first principles atomistics and experiments.

cond-mat.mtrl-sci↗

arXiv2023

Attention-based Multi-fidelity Machine Learning Model for Computational Fractional Flow Reserve Assessment

Coronary Artery Disease (CAD) is one of the most common forms of heart disease, which is caused by a buildup of atherosclerotic plaque (known as stenosis) in the coronary arteries, leading to insufficient supplement of blood, oxygen, and nutrients to the heart. Fractional Flow Reserve (FFR), measuring the pressure ratio between the aorta and distal coronary artery, is an invasive physiologic gold standard for assessing the severity of coronary artery stenosis. Despite its benefits, invasive FFR assessment is still underutilized due to its high cost, time-consuming, experimental variability, and increased risk to patients. In this study, an attention-based multi-fidelity machine learning model (AttMulFid) is proposed for computationally efficient and accurate FFR assessment with uncertainty measurement. Within AttMulFid, an autoencoder is utilized to intelligently select geometric features from coronary arteries, with additional attention on the key area. Results show that the geometric features are able to represent the entirety of the geometric information and intelligently allocate attention based on crucial properties of geometry. Furthermore, the AttMulFid is a feasible approach for non-invasive, rapid, and accurate FFR assessment (with 0.002s/simulation).

cs.CE↗

arXiv2023

Pattern formation in dense populations studied by inference of nonlinear diffusion-reaction mechanisms

Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements that form the basis of this process, like cells and proteins, occupy finite mass and volume and interact during migration. We propose a Reaction-diffusion system with Maxwell-Stefan formulation to construct the diffusive flux. This formulation relies on inter-species force balance and provides a more realistic model for interacting elements. We also present a variational system inference-based technique to extract these models from spatiotemporal data for these processes. We show that the inferred models can capture the characteristics of local Turing instability that instigates the pattern formation process. Moreover, the equilibrium solutions of the inferred models form similar patterns to the observed data.

q-bio.QM↗

arXiv2023

High Order Schemes for Gradient Flow with Respect to a Metric

New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third order consistent, energy stable schemes, which are then demonstrated on several partial differential equations that arise as gradient flow with respect to the 2-Wasserstein metric.

math.NA↗

arXiv2023

A treatment of particle-electrolyte sharp interface fracture in solid-state batteries with multi-field discontinuities

In this work, we present a computational framework for coupled electro-chemo-(nonlinear) mechanics at the particle scale for solid-state batteries. The framework accounts for interfacial fracture between the active particles and solid electrolyte due to intercalation stresses. We extend discontinuous finite element methods for a sharp interface treatment of discontinuities in concentrations, fluxes, electric fields and in displacements, the latter arising from active particle-solid electrolyte interface fracture. We model the degradation in the charge transfer process that results from the loss of contact due to fracture at the electrolyte-active particle interfaces. Additionally, we account for the stress-dependent kinetics that can influence the charge transfer reactions and solid state diffusion. The discontinuous finite element approach does not require a conformal mesh. This offers the flexibility to construct arbitrary particle shapes and geometries that are based on design, or are obtained from microscopy images. The finite element mesh, however, can remain Cartesian, and independent of the particle geometries. We demonstrate this computational framework on micro-structures that are representative of solid-sate batteries with single and multiple anode and cathode particles.

cond-mat.mtrl-sci↗

arXiv2023

FP-IRL: Fokker--Planck Inverse Reinforcement Learning -- A Physics-Constrained Approach to Markov Decision Processes

Inverse reinforcement learning (IRL) is a powerful paradigm for uncovering the incentive structure that drives agent behavior, by inferring an unknown reward function from observed trajectories within a Markov decision process (MDP). However, most existing IRL methods require access to the transition function, either prescribed or estimated \textit{a priori}, which poses significant challenges when the underlying dynamics are unknown, unobservable, or not easily sampled. We propose Fokker--Planck inverse reinforcement learning (FP-IRL), a novel physics-constrained IRL framework tailored for systems that can be described by Fokker--Planck (FP) dynamics. FP-IRL simultaneously infers both the reward and transition functions directly from trajectory data, without requiring access to sampled transitions. Our method leverages a correspondence between MDPs and the FP equation, linking reward maximization in MDPs with free energy minimization in FP dynamics. This connection enables inference of the FP potential function using our inference approach of variational system identification, from which the full set of MDP components -- reward, transition, and policy -- can be recovered using analytic expressions. We demonstrate the effectiveness of FP-IRL through experiments on synthetic benchmarks and a modified version of the Mountain Car problem. Our results show that FP-IRL achieves accurate recovery of agent incentives while preserving computational efficiency and physical interpretability.

cs.LG↗