Akshay Govind Srinivasan

Sahil Girhepuje, Siva Sankar Sajeev, Purvam Jain et al.

Large Language Models (LLMs) currently struggle with tool invocation and chaining, as they often hallucinate or miss essential steps in a sequence. We propose RE-GAINS and EnChAnT, two novel frameworks that empower LLMs to tackle complex user queries by making API calls to external tools based on tool descriptions and argument lists. Tools are chained based on the expected output, without receiving the actual results from each individual call. EnChAnT, an open-source solution, leverages an LLM format enforcer, OpenChat 3.5 (an LLM), and ToolBench's API Retriever. RE-GAINS utilizes OpenAI models and embeddings with a specialized prompt based on the $\underline{R}$easoning vi$\underline{a}$ $\underline{P}$lanning $(RAP)$ framework. Both frameworks are low cost (0.01\$ per query). Our key contribution is enabling LLMs for tool invocation and chaining using modifiable, externally described tools.

Akshay Govind Srinivasan, Balaji Srinivasan

Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times, Physics-Informed Extreme Learning Machines (PIELMs) offer a rapid, closed-form linear solution but are fundamentally limited by physics-agnostic, random initialization. We introduce the Gaussian Mixture Model Adaptive PIELM (GMM-PIELM), a probabilistic framework that learns a probability density function representing the ``location of physics'' for adaptively sampling kernels of PIELMs. By employing a weighted Expectation-Maximization (EM) algorithm, GMM-PIELM autonomously concentrates radial basis function centers in regions of high numerical error, such as shock fronts and boundary layers. This approach dynamically improves the conditioning of the hidden layer without the expensive gradient-based optimization(of PINNs) or Bayesian search. We evaluate our methodology on 1D singularly perturbed convection-diffusion equations with diffusion coefficients $ν=10^{-4}$. Our method achieves $L_2$ errors up to $7$ orders of magnitude lower than baseline RBF-PIELMs, successfully resolving exponentially thin boundary layers while retaining the orders-of-magnitude speed advantage of the ELM architecture.

Akshay Govind Srinivasan, Vikas Dwivedi, Balaji Srinivasan

Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators and complex, hard-to-mesh geometries. Recently developed physics-informed neural networks (PINNs) and their variants are mesh-free and flexible, yet compute-intensive and often less accurate. This paper systematically benchmarks RBF-PIELM, a rapid PINN variant-an extreme learning machine with radial-basis activations-for higher-order PDEs. RBF-PIELM replaces PINNs' time-consuming gradient descent with a single-shot least-squares solve. We test RBF-PIELM on the fourth-order biharmonic equation using two benchmarks: lid-driven cavity flow (streamfunction formulation) and a manufactured oscillatory solution. Our results show up to $(350\times)$ faster training than PINNs and over $(10\times)$ fewer parameters for comparable solution accuracy. Despite surpassing PINNs, RBF-PIELM still lags mature mesh-based solvers and its accuracy degrades on highly oscillatory solutions, highlighting remaining challenges for practical deployment.

Akshay Govind Srinivasan, Anuj Jagannath Said, Sathwik Pentela et al.

Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning. However they remain computationally expensive due to their iterative gradient descent based optimization and scale poorly with increasing model size. This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs. PIELMs replace iterative optimization with a single least-squares solve, enabling deterministic and efficient training. We benchmark PIELM on the Black-Scholes and Heston-Hull-White models for forward pricing and demonstrate its capability in inverse model calibration to recover volatility and interest rate parameters from noisy data. From experiments we observe that PIELM achieve accuracy comparable to PINNs while being up to $30\times$ faster, highlighting their potential for real-time financial modeling.

Akshay Govind Srinivasan, Ryan Jacob George, Jayden Koshy Joe et al.

Accurate and reliable knowledge retrieval is vital for financial question-answering, where continually updated data sources and complex, high-stakes contexts demand precision. Traditional retrieval systems rely on a single database and retriever, but financial applications require more sophisticated approaches to handle intricate regulatory filings, market analyses, and extensive multi-year reports. We introduce a framework for financial Retrieval Augmented Generation (RAG) that leverages agentic AI and the Multi-HyDE system, an approach that generates multiple, nonequivalent queries to boost the effectiveness and coverage of retrieval from large, structured financial corpora. Our pipeline is optimized for token efficiency and multi-step financial reasoning, and we demonstrate that their combination improves accuracy by 11.2% and reduces hallucinations by 15%. Our method is evaluated on standard financial QA benchmarks, showing that integrating domain-specific retrieval mechanisms such as Multi-HyDE with robust toolsets, including keyword and table-based retrieval, significantly enhances both the accuracy and reliability of answers. This research not only delivers a modular, adaptable retrieval framework for finance but also highlights the importance of structured agent workflows and multi-perspective retrieval for trustworthy deployment of AI in high-stakes financial applications.