arXiv subjects

Rahul Gulati

Publications and source records attributed to Rahul Gulati.

5 recordsLinked to original sources

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↗

arXiv2024

Electro-diffusive modeling and the role of spine geometry on action potential propagation in neurons

Electrical signaling in the brain plays a vital role to our existence but at the same time, the fundamental mechanism of this propagation is undeciphered. Notable advancements have been made in the numerical modeling supplementing the related experimental findings. Cable theory based models provided a significant breakthrough in understanding the mechanism of electrical propagation in the neuronal axons. Cable theory, however, fails for thin geometries such as a spine or a dendrite of a neuron, amongst its other limitations. Recently, the spatiotemporal propagation has been precisely modeled using the Poisson-Nernst-Planck (PNP) electro-diffusive theory in the neuronal axons as well as the dendritic spines respectively. Patch clamp and voltage imaging experiments have extensively aided the study of action potential propagation exclusively for the neuronal axons but not the dendritic spines because of the challenges linked with their thin geometry. Assisted by the super-resolution microscopes and the voltage dyeing experiments, it has become possible to precisely measure the voltage in the dendritic spines. This has facilitated the requirement of a high fidelity numerical frame that is capable of acting as a digital twin. Here, using the PNP theory, we integrate the dendritic spine, soma and the axon region to numerically model the propagation of excitatory synaptic potential in a complete neuronal geometry with the synaptic input at the spines, potential initiating at the axon hillock and propagating through the neuronal axon. The model outputs the forward propagation of the action potential along the neuronal axons as well as the back propagation into the spines. We point out the significance of the intricate geometry of the dendritic spines, namely the spine neck length and radius, and the ion channel density in the axon hillock to the action potential initiation and propagation.

q-bio.NC↗

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↗

arXiv2022

Spatio-temporal modeling of saltatory conduction in neurons using Poisson-Nernst-Planck treatment and estimation of conduction velocity

Action potential propagation along the axons and across the dendrites is the foundation of the electrical activity observed in the brain and the rest of the central nervous system. Theoretical and numerical modeling of this action potential activity has long been a key focus area of electro-chemical neuronal modeling. Specifically, considering the presence of nodes of Ranvier along the myelinated axon, single-cable models of the propagation of action potential have been popular. Building on these models, and considering a secondary electrical conduction pathway below the myelin sheath, the double-cable model has been proposed. Such cable theory based treatments have inherent limitations in their lack of a representation of the spatio-temporal evolution of the neuronal electro-chemistry. In contrast, a Poisson-Nernst-Planck (PNP) based electro-diffusive framework accounts for the underlying spatio-temporal ionic concentration dynamics and is a more comprehensive treatment. In this work, a high-fidelity implementation of the PNP model is demonstrated. This model is shown to produce results similar to the cable theory based electrical models, and in addition, the rich spatio-temporal evolution of the underlying ionic transport is captured. Novel to this work is the extension of PNP model to axonal geometries with multiple nodes of Ranvier and multiple variants of the electro-diffusive model - PNP without myelin, PNP with myelin, and PNP with the myelin sheath and peri-axonal space. Further, we apply this spatio-temporal model to numerically estimate conduction velocity in a rat axon. Specifically, saltatory conduction due to the presence of myelin sheath and the peri-axonal space is investigated.

q-bio.QM↗

arXiv2021

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging of nutrients, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modeling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model symmetry breaking deformations and structural bifurcations. To address this limitation, a 3D computational mechanics framework for high fidelity modeling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy based mechanics, and state-of-the-art numerical techniques for modeling deformation of surface geometries. Lipid bilayers are represented as spline-based surfaces immersed in a 3D space; this enables modeling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a 3D space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modeling 3 classical, yet non-trivial, membrane problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full 3D membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a "phase diagram" for its symmetric and broken-symmetry states.

q-bio.QM↗