Janak M. Patel

Janak M. Patel, Anirudh Deodhar, Dagnachew Birru

Demand forecasting at the bottom of a retail hierarchy requires predicting tens of thousands of correlated long-horizon series across products, stores, and regions. Modern systems must scale across massive catalogs, capture shared demand dynamics, and remain interpretable enough to be trusted. Classical statistical methods need a separate model per series and are hard to manage at scale; deep autoregressive models struggle as the joint state grows to tens of thousands of dimensions; and recent graph-based forecasters, while capturing cross-entity dependencies, often produce opaque long-horizon forecasts. We propose GNBAN (Graph Neural Basis Attention Network), an end-to-end architecture combining heterogeneous graph representation learning with an interpretable basis-decomposition head. Retail data are represented directly as a heterogeneous graph derived from the relational schema, so a single model serves the entire catalog. Rather than predicting the horizon directly, GNBAN decomposes each forecast into trend, seasonal, and generic components. Its key innovation is a per-basis attention mechanism: each basis function keeps its own learnable query and retrieves information independently from the entity's historical neighborhood, letting different bases specialize to distinct temporal patterns while preserving interpretability. On two large-scale benchmarks, M5 Walmart and Favorita Grocery Sales, evaluated under matched protocols, GNBAN improves volume-weighted WRMSSE by roughly 4-5% over a matched graph baseline. Qualitative analysis shows the learned decomposition exposes trend, seasonal, and residual demand drivers without post-hoc explanation methods. These results demonstrate that scalable relational forecasting and interpretable forecast decomposition can be achieved together in a unified graph-based framework.

Milad Ramezankhani, Janak M. Patel, Anirudh Deodhar et al.

We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems defined on irregular geometries and non-uniform meshes. GITO consists of two main modules: a hybrid graph transformer (HGT) and a transformer neural operator (TNO). HGT leverages a graph neural network (GNN) to encode local spatial relationships and a transformer to capture long-range dependencies. A self-attention fusion layer integrates the outputs of the GNN and transformer to enable more expressive feature learning on graph-structured data. TNO module employs linear-complexity cross-attention and self-attention layers to map encoded input functions to predictions at arbitrary query locations, ensuring discretization invariance and enabling zero-shot super-resolution across any mesh. Empirical results on benchmark PDE tasks demonstrate that GITO outperforms existing transformer-based neural operators, paving the way for efficient, mesh-agnostic surrogate solvers in engineering applications.

Janak M. Patel, Milad Ramezankhani, Anirudh Deodhar et al.

Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive simulations, such as finite element analysis, and the complexity of rigorous optimization algorithms. Data-agnostic AI-based surrogate models, such as Physics-Informed Neural Operators (PINOs), offer a promising alternative to these conventional simulations, providing drastically reduced inference time, unparalleled data efficiency, and zero-shot super-resolution capability. However, the predictive accuracy of these models is often constrained to small, low-dimensional design spaces or systems with relatively simple dynamics. To address this, we introduce a novel Physics-Informed DeepONet (PIDON) architecture, which extends the capabilities of conventional neural operators to effectively model the nonlinear behavior of complex engineering systems across high-dimensional design spaces and a wide range of dynamic design configurations. This new architecture outperforms existing SOTA models, enabling better predictions across broader design spaces. Leveraging PIDON's differentiability, we integrate a gradient-based optimization approach using the Adam optimizer to efficiently determine optimal design variables. This forms an end-to-end gradient-based optimization framework that accelerates the design process while enhancing scalability and efficiency. We demonstrate the effectiveness of this framework in the optimization of aerospace-grade composites curing processes achieving a 3x speedup in obtaining optimal design variables compared to gradient-free methods. Beyond composites processing, the proposed model has the potential to be used as a scalable and efficient optimization tool for broader applications in advanced engineering and digital twin systems.

Janak M. Patel, Milad Ramezankhani, Anirudh Deodhar et al.

The rapid adoption of battery-powered vehicles and energy storage systems over the past decade has made battery health monitoring increasingly critical. Batteries play a central role in the efficiency and safety of these systems, yet they inevitably degrade over time due to repeated charge-discharge cycles. This degradation leads to reduced energy efficiency and potential overheating, posing significant safety concerns. Accurate estimation of a State of Health (SoH) of battery is therefore essential for ensuring operational reliability and safety. Several machine learning architectures, such as LSTMs, transformers, and encoder-based models, have been proposed to estimate SoH from discharge cycle data. However, these models struggle with the irregularities inherent in real-world measurements: discharge readings are often recorded at non-uniform intervals, and the lengths of discharge cycles vary significantly. To address this, most existing approaches extract features from the sequences rather than processing them in full, which introduces information loss and compromises accuracy. To overcome these challenges, we propose a novel architecture: Time-Informed Dynamic Sequence Inverted Transformer (TIDSIT). TIDSIT incorporates continuous time embeddings to effectively represent irregularly sampled data and utilizes padded sequences with temporal attention mechanisms to manage variable-length inputs without discarding sequence information. Experimental results on the NASA battery degradation dataset show that TIDSIT significantly outperforms existing models, achieving over 50% reduction in prediction error and maintaining an SoH prediction error below 0.58%. Furthermore, the architecture is generalizable and holds promise for broader applications in health monitoring tasks involving irregular time-series data.