Raghav Gnanasambandam

Raghav Gnanasambandam, Bo Shen, Jihoon Chung et al.

Physics-informed Neural Networks (PINNs) are gaining attention in the engineering and scientific literature for solving a range of differential equations with applications in weather modeling, healthcare, manufacturing, etc. Poor scalability is one of the barriers to utilizing PINNs for many real-world problems. To address this, a Self-scalable tanh (Stan) activation function is proposed for the PINNs. The proposed Stan function is smooth, non-saturating, and has a trainable parameter. During training, it can allow easy flow of gradients to compute the required derivatives and also enable systematic scaling of the input-output mapping. It is shown theoretically that the PINNs with the proposed Stan function have no spurious stationary points when using gradient descent algorithms. The proposed Stan is tested on a number of numerical studies involving general regression problems. It is subsequently used for solving multiple forward problems, which involve second-order derivatives and multiple dimensions, and an inverse problem where the thermal diffusivity of a rod is predicted with heat conduction data. These case studies establish empirically that the Stan activation function can achieve better training and more accurate predictions than the existing activation functions in the literature.

Yutao Du, Qin Li, Raghav Gnanasambandam et al.

Exploring the outer atmosphere of the sun has remained a significant bottleneck in astrophysics, given the intricate magnetic formations that significantly influence diverse solar events. Magnetohydrodynamics (MHD) simulations allow us to model the complex interactions between the sun's plasma, magnetic fields, and the surrounding environment. However, MHD simulation is extremely time-consuming, taking days or weeks for simulation. The goal of this study is to accelerate coronal magnetic field simulation using deep learning, specifically, the Fourier Neural Operator (FNO). FNO has been proven to be an ideal tool for scientific computing and discovery in the literature. In this paper, we proposed a global-local Fourier Neural Operator (GL-FNO) that contains two branches of FNOs: the global FNO branch takes downsampled input to reconstruct global features while the local FNO branch takes original resolution input to capture fine details. The performance of the GLFNO is compared with state-of-the-art deep learning methods, including FNO, U-NO, U-FNO, Vision Transformer, CNN-RNN, and CNN-LSTM, to demonstrate its accuracy, computational efficiency, and scalability. Furthermore, physics analysis from domain experts is also performed to demonstrate the reliability of GL-FNO. The results demonstrate that GL-FNO not only accelerates the MHD simulation (a few seconds for prediction, more than \times 20,000 speed up) but also provides reliable prediction capabilities, thus greatly contributing to the understanding of space weather dynamics. Our code implementation is available at https://github.com/Yutao-0718/GL-FNO

Xinyun Huo, Raghav Gnanasambandam, Xinyao Zhang

Human-robot collaboration in industrial settings requires precise and reliable communication to enhance operational efficiency. While Large Language Models (LLMs) understand general language, they often lack the domain-specific rigidity needed for safe and executable industrial commands. To address this gap, this paper introduces a novel grammar-constrained LLM that integrates a grammar-driven Natural Language Understanding (NLU) system with a fine-tuned LLM, which enables both conversational flexibility and the deterministic precision required in robotics. Our method employs a two-stage process. First, a fine-tuned LLM performs high-level contextual reasoning and parameter inference on natural language inputs. Second, a Structured Language Model (SLM) and a grammar-based canonicalizer constrain the LLM's output, forcing it into a standardized symbolic format composed of valid action frames and command elements. This process guarantees that generated commands are valid and structured in a robot-readable JSON format. A key feature of the proposed model is a validation and feedback loop. A grammar parser validates the output against a predefined list of executable robotic actions. If a command is invalid, the system automatically generates corrective prompts and re-engages the LLM. This iterative self-correction mechanism allows the model to recover from initial interpretation errors to improve system robustness. We evaluate our grammar-constrained hybrid model against two baselines: a fine-tuned API-based LLM and a standalone grammar-driven NLU model. Using the Human Robot Interaction Corpus (HuRIC) dataset, we demonstrate that the hybrid approach achieves superior command validity, which promotes safer and more effective industrial human-robot collaboration.