21 papers
SciML in the Wild: A Diagnostic Study of When Structural Priors Help and When They Hurt
Vrishank Sai Anand, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar +2
Scientific Machine Learning (SciML) methods such as Neural Ordinary Differential Equations (NODEs), Physics-Informed Neural Networks (PINNs), and Universal Differential Equations (…
Beyond Passive Viewing: A Pilot Study of a Hybrid Learning Platform Augmenting Video Lectures with Conversational AI
Mohammed Abraar, Raj Abhijit Dandekar, Rajat Dandekar +1
The exponential growth of AI education has brought millions of learners to online platforms, yet this massive scale has simultaneously exposed critical pedagogical shortcomings. Tr…
Three methods, one problem: Classical and AI approaches to no-three-in-line
Pranav Ramanathan, Thomas Prellberg, Matthew Lewis +4
The No-Three-In-Line problem asks for the maximum number of points that can be placed on an n by n grid with no three collinear, representing a famous problem in combinatorial geom…
Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations
Suriya R S, Prathamesh Dinesh Joshi, Rajat Dandekar +2
The n body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learni…
Adaptive tumor growth forecasting via neural & universal ODEs
Kavya Subramanian, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar +2
Forecasting tumor growth is critical for optimizing treatment. Classical growth models such as the Gompertz and Bertalanffy equations capture general tumor dynamics but may fail to…
Physics-Informed Neural ODEs with Scale-Aware Residuals for Learning Stiff Biophysical Dynamics
Kamalpreet Singh Kainth, Prathamesh Dinesh Joshi, Raj Abhijit Dandekar +2
Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs a…