arXiv subjects

Siddharth Prabhu

Publications and source records attributed to Siddharth Prabhu.

5 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

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↗

arXiv2016

OPE convergence in non-relativistic conformal field theories

Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NRCFT, in particular the mapping between operators and states in a non-relativistic "radial quantization" Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2,d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.

hep-th↗

arXiv2015

Simultaneous B and L Violation: New Signatures from RPV-SUSY

Studies of R-parity violating (RPV) supersymmetry typically assume that nucleon stability is protected by approximate baryon number (B) or lepton number (L) conservation. We present a new class of RPV models that violate B and L simultaneously (BLRPV), without inducing rapid nucleon decay. These models feature an approximate $Z_2^e \times Z_2^μ\times Z_2^τ$ flavor symmetry, which forbids 2-body nucleon decay and ensures that flavor antisymmetric $L L E^c$ couplings are the only non-negligible L-violating operators. Nucleons are predicted to decay through $N \rightarrow K e μν$ and $n \rightarrow e μν$; the resulting bounds on RPV couplings are rather mild. Novel collider phenomenology arises because the superpartners can decay through both L-violating and B-violating couplings. This can lead to, for example, final states with high jet multiplicity and multiple leptons of different flavor, or a spectrum in which depending on the superpartner, either B or L violating decays dominate. BLRPV can also provide a natural setting for displaced $\tildeν \rightarrow μe$ decays, which evade many existing collider searches for RPV supersymmetry.

hep-ph↗