In [1], we model an industrial dryer using a neural partial differential equation (PDE) and train it using partially observed measurements. We also develop a fully differentiable ODE solver capable of handling events in parallel. Despite being trained on partially observed and sparse measurements, we observe that incorporating physics into a flexible neural network helps generalize to unseen process conditions. Furthermore, we use this trained model to generate energy-optimized recipes.
In [2], we introduce an integral formulation of the SINDy method that not only discovers the parameters but also estimates the parameters while preserving convexity. We also show that incorporating domain knowledge, such as mass balance and chemistry information, makes the entire process more robust towards noisy, real-time measurements. In [3] we extend the previous integral formulation to a more general class of nonconvex parameter estimation and model discovery problems. We use a bi-level optimization method that exploits the convexity of certain parameters given the remaining parameters. Using benchmark problems from chemical reaction and biological systems engineering, we show that this approach has a wider area of convergence than conventional sequential optimization methods.
Neural ordinary differential equations (NODEs) have become a very popular approach for learning unknown dynamics from measurements and for efficiently estimating sensitivities in parameter estimation. However, training them is often unstable, especially for very long and chaotic trajectories. To overcome this issue, in [4], we introduce multiple-shooting neural ordinary differential equations (MS-NODE), which is a more stable alternative for training NODE on oscillatory trajectories. We develop a condensing-based approach to incorporate general equality constraints while training a neural network using first-order optimization methods. This approach can not only deal with the continuity constraints arising in a multiple-shooting problem but also general equality constraints. We validate our algorithm on highly nonlinear and oscillatory dynamics.
Other projects include developing an interior-point differential dynamic programming (DDP) approach for solving optimal control problems [5], and building a reduced-order model for a cardiovascular system for use in model predictive control [6].
In most of these projects, we use JAX, which is an automatic differentiation library in Python. JAX plays a crucial role in defining custom differentiation rules for a range of challenging problems - ordinary differential equations with events, ordinary differential equations with recirculation, root-finding problems, bi-level optimization problems, and problems involving sparse Jacobians. By exploiting problem structure within JAX, we achieve significant improvements in computational performance.
Research Interests: Scientific Machine Learning, Parameter estimation, Performance-focused differentiable programming for scientific computing tasks.
References :
[1] S Prabhu, S Haque, D Gurr, L Coley, J Beilstein, S Rangarajan, and M Kothare. An event-based neural partial differential equation model of heat and mass transport in an industrial drying oven. Computers & Chemical Engineering, page 109171, 2025.
[2] S Prabhu, N Kosir, M V Kothare, and S Rangarajan. Derivative-free domain-informed data-driven discovery of sparse kinetic models. Industrial & Engineering Chemistry Research, 2025.
[3] S Prabhu, S Rangarajan, and M Kothare. Bi-level optimization for parameter estimation of differential equations using interpolation, 2025.
[4] S Prabhu, S Rangarajan, and M Kothare. A condensing approach to multiple shooting neural ordinary differential equation, 2025.
[5] S Prabhu, S Rangarajan, and M Kothare. Differential dynamic programming with stagewise equality and inequality constraints using interior point method. arXiv preprint arXiv:2409.12048, 2024.
[6] S Prabhu, S Rangarajan, and M Kothare. Data-driven discovery of sparse dynamical model of cardiovascular system for model predictive control. Computers in biology and medicine, 166:107513, 2023.