Pratik Rathore

I recently graduated from Stanford University with a PhD in Electrical Engineering, advised by Madeleine Udell. I am currently interning at a stealth startup in the energy sector, and will start as a quantitative researcher at Citadel Securities in Fall 2026.

Before Stanford, I graduated from the University of Maryland with a double degree in Electrical Engineering and Mathematics.

During my PhD, I have interned at Skyworks Solutions, where I worked on AI-driven circuit design automation, and at Gridmatic, where I worked on faster optimization for battery scheduling and price impact models for energy trading.

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Earlier in my PhD, I leveraged techniques from randomized numerical linear algebra and stochastic optimization to design fast, scalable optimization algorithms for training machine learning models. Later in my PhD, I became interested in scientific machine learning, particularly focusing on challenges and applications of physics-informed neural networks and operator learning.

^* denotes equal contribution.

Full waveform inversion (FWI) is the gold standard for subsurface imaging, but is computationally expensive. Machine learning (ML) is promising for accelerating FWI, but ML-based approaches need field-scale, geologically diverse, and physically realistic datasets, which are unavailable in the literature. We address these limitations with SubsurfaceGen, a GPU-accelerated generator for 3D velocity models and seismic data, which we use to create a field-scale, geologically diverse, physically realistic dataset (available on Hugging Face). Our experiments on this dataset demonstrate SubsurfaceGen's potential to accelerate the development of ML-based FWI methods.

We develop an approximate, distributed, accelerated sketch-and-project method that scales Gaussian process inference to hundreds of millions of samples.

We develop ASkotch, a scalable, accelerated, iterative method for full kernel ridge regression (KRR) that provably obtains linear convergence. ASkotch outperforms state-of-the-art KRR solvers on a testbed of 23 large-scale KRR regression and classification tasks derived from a wide range of application domains. Our work opens up the possibility of as-yet-unimagined applications of full KRR across a number of disciplines.

We study challenges in training physics-informed neural networks. We link training issues to ill-conditioning of the loss, and show a combined Adam and L-BFGS approach, along with a new optimizer, NysNewton-CG, enhances PINN performance.

We propose PROMISE, a family of preconditioned stochastic optimization methods that use scalable, randomized curvature estimates to solve large-scale, ill-conditioned convex optimization problems in machine learning. PROMISE methods, with default hyperparameters, outperform popular tuned stochastic optimizers on ridge and logistic regression. Furthermore, we introduce quadratic regularity, which determines the speed of linear convergence for PROMISE methods and allows us to obtain improved rates for ridge regresison.

We use techniques from randomized numerical linear algebra to develop a fast, scalable, preconditioned stochastic gradient method for convex machine learning problems.

We prove new results regarding the prime factorizations of Descartes numbers, a family of odd spoof perfect numbers.

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