Ruchi Sandilya

I am a postdoctoral researcher in the Grosenick Lab at Weill Cornell Medicine, working at the intersection of applied mathematics, control theory, and scientific machine learning. My research focuses on developing mathematically grounded machine learning methods for modeling, interpreting, and controlling complex dynamical systems in the physical and biological sciences.

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Selected Research Projects

    Contrastive Diffusion Alignment (ConDA) — 2026

    My recent work develops interpretable and controllable generative models for complex dynamical systems in physics and biomedicine. I introduced Contrastive Diffusion Alignment (ConDA), a framework that combines contrastive learning with pretrained diffusion models to organize latent spaces around meaningful physical, biological, and behavioral dynamics. This alignment enables interpretable nonlinear trajectory editing and high-fidelity controllable generation across applications including fluid dynamics, neural activity, facial behavior, and therapeutic neurostimulation. This work advances the development of generative scientific surrogates and data-driven digital twins for forecasting, counterfactual analysis, and scientific discovery.
    Paper    Poster    GitHub Code

    Quantized Graph Convolution Networks (QGCN) — 2024

    We introduced Quantized Graph Convolution Networks (QGCNs), a framework extending CNNs to graph-structured data such as biological and social networks. QGCNs decompose convolutions into non-overlapping sub-kernels that adapt naturally to irregular graph domains while retaining the strengths of CNN architectures. Integrated within a residual network, QGCNs generalize to graphs of arbitrary size and dimension through a learnable multinomial assignment mechanism. The model achieves state-of-the-art performance on benchmark graph datasets and is particularly effective for predicting nonlinear dynamics on finite-element graphs, providing a powerful architecture for scientific machine learning on irregular domains.
    Paper    Poster    GitHub Code

    Feedback Stabilization of the Boussinesq System — 2021

    In this project, I developed feedback control laws for stabilizing unstable buoyancy-driven fluid flows governed by the Boussinesq equations. By projecting the linearized system onto unstable modes and solving a low-dimensional Riccati equation, we derived boundary feedback controllers that stabilize velocity and temperature dynamics. This work demonstrates how control-theoretic model reduction can regulate nonlinear fluid systems, with applications in energy-efficient ventilation, climate control, and aerospace environmental systems.
    Paper    Slides    GitHub Code

    Discontinuous Finite Volume Methods for PDE-Constrained Optimal Control — 2017

    During my PhD, I developed and analyzed discontinuous finite-volume methods for PDE-constrained optimal control problems with pointwise control constraints. The framework addressed elliptic, parabolic, hyperbolic, and Brinkman flow systems using an optimize-then-discretize approach. I derived a priori error estimates and optimal convergence guarantees, and validated them through numerical experiments. These methods were applied to problems in biomedical modeling, drug transport, fluid mechanics, and energy systems, establishing reliable numerical foundations for control of complex multiphysics systems.
    Ph.D. Thesis    Slides