arXiv subjects

Srinivas Rangarajan

Publications and source records attributed to Srinivas Rangarajan.

7 recordsLinked to original sources

arXiv2026

Bi-Level optimization for interpolation-based parameter estimation of differential equations

Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization formulation, is commonplace in chemical engineering applications. A popular method for parameter estimation is sequential optimization (single-shooting), which numerically integrates the ODE in each iteration. However, computing the gradients for the optimization steps requires calculating sensitivities, i.e., the derivatives of states with respect to the parameters, through the numerical integrator, which can be computationally expensive. In this work, we use interpolation to reduce the cost of these sensitivity calculations. Leveraging this interpolation, we also propose a bi-level optimization framework that exploits the structure of the differential equations and solves a convex inner problem. We apply this framework to examples spanning conventional parameter estimation and the emerging concept of data-driven dynamic model discovery. We show that our approach not only estimates the correct parameters for benchmark problems, but can also be readily extended to delay, stiff, and partially observed differential equations without major modifications.

eess.SY↗

arXiv2025

A condensing approach to multiple shooting neural ordinary differential equation

Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied to eliminate the shooting gap between the end of the previous trajectory and the start of the next trajectory. Unlike single-shooting, multiple-shooting is more stable, especially for highly oscillatory and long trajectories. In the context of neural ordinary differential equations, multiple-shooting is not widely used due to the challenge of incorporating general equality constraints. In this work, we propose a condensing-based approach to incorporate these shooting equality constraints while training a multiple-shooting neural ordinary differential equation (MS-NODE) using first-order optimization methods such as Adam.

cs.LG↗

arXiv2024

A High-Throughput and Data-Driven Computational Framework for Novel Quantum Materials

Two-dimensional layered materials, such as transition metal dichalcogenides (TMDs), possess intrinsic van der Waals gap at the layer interface allowing for remarkable tunability of the optoelectronic features via external intercalation of foreign guests such as atoms, ions, or molecules. Herein, we introduce a high-throughput, data-driven computational framework for the design of novel quantum materials derived from intercalating planar conjugated organic molecules into bilayer transition metal dichalcogenides and dioxides. By combining first-principles methods, material informatics, and machine learning, we characterize the energetic and mechanical stability of this new class of materials and identify the fifty (50) most stable hybrid materials from a vast configurational space comprising $\sim 10^5$ materials, employing intercalation energy as the screening criterion.

cond-mat.mtrl-sci↗

arXiv2024

Differential dynamic programming with stagewise equality and inequality constraints using interior point method

Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as augmented lagrangian methods, active set methods, and barrier methods. In this paper, we use an interior point method, which is a type of barrier method, to incorporate arbitrary stagewise equality and inequality state and control constraints. We also provide explicit update formulas for all the involved variables. Finally, we apply this algorithm to example systems such as the inverted pendulum, a continuously stirred tank reactor, car parking, and obstacle avoidance.

math.OC↗

arXiv2021

Self-learn to Explain Siamese Networks Robustly

Learning to compare two objects are essential in applications, such as digital forensics, face recognition, and brain network analysis, especially when labeled data is scarce and imbalanced. As these applications make high-stake decisions and involve societal values like fairness and transparency, it is critical to explain the learned models. We aim to study post-hoc explanations of Siamese networks (SN) widely used in learning to compare. We characterize the instability of gradient-based explanations due to the additional compared object in SN, in contrast to architectures with a single input instance. We propose an optimization framework that derives global invariance from unlabeled data using self-learning to promote the stability of local explanations tailored for specific query-reference pairs. The optimization problems can be solved using gradient descent-ascent (GDA) for constrained optimization, or SGD for KL-divergence regularized unconstrained optimization, with convergence proofs, especially when the objective functions are nonconvex due to the Siamese architecture. Quantitative results and case studies on tabular and graph data from neuroscience and chemical engineering show that the framework respects the self-learned invariance while robustly optimizing the faithfulness and simplicity of the explanation. We further demonstrate the convergence of GDA experimentally.

cs.LG↗

arXiv2019

Designing compact training sets for data-driven molecular property prediction

In this paper, we consider the problem of designing a training set using the most informative molecules from a specified library to build data-driven molecular property models. Specifically, we use (i) sparse generalized group additivity and (ii) kernel ridge regression as two representative classes of models, we propose a method combining rigorous model-based design of experiments and cheminformatics-based diversity-maximizing subset selection within the epsilon--greedy framework to systematically minimize the amount of data needed to train these models. We demonstrate the effectiveness of the algorithm on subsets of various databases, including QM7, NIST, and a catalysis dataset. For sparse group additive models, a balance between exploration (diversity-maximizing selection) and exploitation (D-optimality selection) leads to learning with a fraction (sometimes as little as 15%) of the data to achieve similar accuracy as five-fold cross validation on the entire set. On the other hand, kernel ridge regression prefers diversity-maximizing selections.

physics.data-an↗

arXiv2019

On Deriving Probabilistic Models for Adsorption Energy on Transition Metals using Multi-level Ab initio and Experimental Data

In this paper, we apply multi-task Gaussian Process (MT-GP) to show that the adsorption energy of small adsorbates on transition metal surfaces can be modeled to a high level of fidelity using data from multiple sources, taking advantage of the relatively abundant ''low fidelity" data (such as from density functional theory computations) and small amounts of ''high fidelity" computational (e.g. using the random phase approximation) or experimental data. To fully explore the performance of MT-GP, we perform two case studies - one using purely computational datasets and the other using a combination of experimental and computational datasets. In both cases, the performance of MT-GPs is significantly better than single-task models built on a single data source. This method can be used to learn improved models from fused datasets, and thereby build accurate models under tight computational and experimental budget.

physics.data-an↗