Dagnachew Birru

Milad Ramezankhani, Rishi Yash Parekh, Anirudh Deodhar et al.

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large datasets for effective training. While physics-informed operators offer a data-agnostic learning approach, they introduce additional training complexities and convergence issues, especially in highly nonlinear systems. To overcome these challenges, we introduce Finite Basis Physics-Informed HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic domain decomposition. By leveraging hypernetworks and finite basis functions, FB-HyDON effectively mitigates the training limitations associated with existing physics-informed operator learning methods. We validated our approach on the high-frequency harmonic oscillator, Burgers' equation at different viscosity levels, and Allen-Cahn equation demonstrating substantial improvements over other operator learning models.

Vipul Patel, Anirudh Deodhar, Dagnachew Birru

Workforce scheduling is an NP-hard combinatorial optimization problem requiring simultaneous satisfaction of labor regulations, coverage requirements, employee preferences and operational objectives. Existing CP formulations typically model simplified instances with 6-12 constraints at shift-level granularity and critically lack explicit support for: mandatory break scheduling with midpoint placement control; acuity weighted workload equity; sub-shift temporal granularity enabling demand-driven staffing; inter-week schedule stability; and cross-midnight shift patterns common in 24-hour operations. This paper presents CP-WSP: a declarative CP-SAT framework enforcing 14 hard constraints as mathematically inviolable requirements (zero regulatory violations by construction) while optimizing 15 soft objectives through a unified weighted penalty function -- all configurable via a JSON specification with no code changes required. Key contributions include: a shift-window variable decomposition enabling mandatory break scheduling with centrality control; acuity-weighted workload equity; multi-granularity temporal resolution from 30 minutes to 2 hours; inter-week schedule stability; a grid-offset preprocessing technique for cross-midnight shifts; and a reproducible 36-configuration benchmark suite for community comparison. Evaluated on INRC-II benchmarks at both hourly and shift-level granularity and on 36 synthetic configurations.

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.

Vipul Patel, Anirudh Deodhar, Dagnachew Birru

Workforce scheduling in the healthcare sector is a significant operational challenge, characterized by fluctuating patient loads, diverse clinical skills, and the critical need to control labor costs while upholding high standards of patient care. This problem is inherently multi-objective, demanding a delicate balance between competing goals: minimizing payroll, ensuring adequate staffing for patient needs, and accommodating staff preferences to mitigate burnout. We propose a Multi-objective Genetic Algorithm (MOO-GA) that models the hospital unit workforce scheduling problem as a multi-objective optimization task. Our model incorporates real-world complexities, including hourly appointment-driven demand and the use of modular shifts for a multi-skilled workforce. By defining objective functions for cost, patient care coverage, and staff satisfaction, the GA navigates the vast search space to identify a set of high-quality, non-dominated solutions. Demonstrated on datasets representing a typical hospital unit, the results show that our MOO-GA generates robust and balanced schedules. On average, the schedules produced by our algorithm showed a 66\% performance improvement over a baseline that simulates a conventional, manual scheduling process. This approach effectively manages trade-offs between critical operational and staff-centric objectives, providing a practical decision support tool for nurse managers and hospital administrators.

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.

Milad Ramezankhani, Anirudh Deodhar, Rishi Yash Parekh et al.

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural networks. However, for highly nonlinear real-world applications like aerospace composites processing, existing models often fail to capture underlying solutions accurately and are typically limited to single input functions, constraining rapid process design development. This paper introduces an advanced physics-informed DeepONet tailored for such complex systems with multiple input functions. Equipped with architectural enhancements like nonlinear decoders and effective training strategies such as curriculum learning and domain decomposition, the proposed model handles high-dimensional design spaces with significantly improved accuracy, outperforming the vanilla physics-informed DeepONet by two orders of magnitude. Its zero-shot prediction capability across a broad design space makes it a powerful tool for accelerating composites process design and optimization, with potential applications in other engineering fields characterized by strong nonlinearity.