Ruchi Sandilya

Selected Research Projects

• Nonlinearly Controllable Counterfactuals      WCM (2025)

  In this project, we develop controllable and counterfactual generative models for complex physical systems, personalized healthcare, and explainable AI. Using state-of-the-art generative models, we generate precise, nonlinearly controllable counterfactuals for nonlinear dynamic systems where traditional methods fall short. Validated in applications like flow past a cylinder and TMS-induced electric field modeling, these models leverage numerically simulated benchmarks for scenario testing and optimization without direct experimentation. This work has applications in personalized neurostimulation for treatment-resistant depression and aerodynamic design optimization.

• Generalizing CNNs to graphs with learnable neighborhood quantization      WCM (2024)

  In this project, we introduced Quantized Graph Convolution Networks (QGCNs), a novel framework that extends CNNs to graph data, addressing the challenge of analyzing non-array-structured information such as biological and social networks. QGCNs achieve this by decomposing convolutions into non-overlapping sub-kernels, seamlessly adapting to graph structures while retaining CNN strengths. This approach, integrated into a residual network, generalizes to graphs of any size and dimension through a learnable multinomial assignment mechanism. QGCNs match or exceed state-of-the-art GNNs on benchmark datasets and excel in predicting nonlinear dynamics on finite element graphs, offering a powerful and expressive model for graph-based learning.
  Paper    Poster    GitHub Code
  

• Feedback stabilization of the Boussinesq system      TIFR CAM (2021)

  In this project, we developed feedback control laws to stabilize unstable fluid dynamics in the Boussinesq system, which models non-isothermal fluid flows. Using a projected linearized system and solving a small-dimensional Riccati equation, we demonstrated effective stabilization of flow and temperature. This work has practical applications in optimizing energy use in buildings and aircraft by managing indoor environmental factors, crucial for energy efficiency and emissions reduction. Additionally, the COVID-19 pandemic underscored the importance of indoor air quality, further highlighting the impact of this research.
  Slides    Video
  

• PDE constrained optimal control problems      Ph.D. (2017)

  During my doctoral research, I developed and analyzed discontinuous finite volume methods for solving PDE-constrained optimal control problems under pointwise control constraints. My work covered semilinear elliptic, parabolic, hyperbolic problems, and Brinkman equations, with applications in cancer treatment, drug kinetics, brain dynamics, tissue engineering, aircraft design, and enhanced oil recovery. Using an optimize-then-discretize approach, I explored variational, piecewise constant, and piecewise linear control approximations, deriving a priori error estimates and validating theoretical convergence through numerical experiments. I further extended these methods to hydrocarbon extraction via immiscible fluid injection and blood flow modeling through the myocardium, demonstrating their broad applicability in engineering and biological systems.