Aaditya L. Kachhadiya

Surat, Gujarat, India

I am a high school student and independent researcher who brings together machine learning, physics, and numerical optimization to study how learning systems can become more principled tools for scientific discovery.

My work so far has explored scientific machine learning from several directions, including learned inverse methods for physical systems, optimization in physics-informed models, and diagnostics for understanding when scientific ML methods behave reliably. More broadly, I am interested in developing ideas that connect machine learning with the mathematical and physical structure of the problems it is used to study.

news

Sep 27, 2026	Began research with the CRUNCH Group at Brown University under the mentorship of Prof. George Em Karniadakis and Ruthwik Chivukula.
Sep 25, 2026	Invited to present one of my papers at the CRUNCH Group Weekly Seminar Spotlight, Brown University Department of Applied Mathematics.
Jul 01, 2026	First-author paper on subspace optimization for physics-informed learning submitted to IEEE Transactions on Neural Networks and Learning Systems.
May 15, 2026	New preprint posted: “Local Inverse Geometry Can Be Amortized.” arXiv:2605.13068.

selected publications

IEEE TNNLS

Component-Access Subspace Optimization for Heterogeneous Scalarized Learning

Aaditya Kachhadiya, Meet Dabgar, Tanmoy Hazra, and Anupam Shukla

Manuscript under review, IEEE Transactions on Neural Networks and Learning Systems, 2026
arXiv
Local Inverse Geometry Can Be Amortized

Aaditya L. Kachhadiya

arXiv preprint arXiv:2605.13068, 2026

Abs arXiv Bib Code

Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss–Newton and Levenberg–Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based linearized systems. We propose a learned alternative: amortize local inverse geometry into a reusable reverse operator. Our framework learns a bidirectional surrogate, Deceptron, and deploys it through D-IPG (Deceptron Inverse-Preconditioned Gradient), an iterative solver that pulls residual-corrected measurement-space proposals back to latent space. The key mechanism is a Jacobian Composition Penalty (JCP), which trains the reverse Jacobian to act as a local left inverse of the forward Jacobian; its runtime counterpart, RJCP, measures the same inverse-consistency error along optimization trajectories. We prove that D-IPG is first-order equivalent to damped Gauss–Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning. Across seven PDE inverse-problem benchmarks, D-IPG outperforms standard baselines, achieves 94.8% mean success across the six-problem reliability suite, and reaches comparable or better recovery quality at up to \(77\times\)lower inference-time solve cost on the main benchmarks.
@article{kachhadiya2026local, title = {Local Inverse Geometry Can Be Amortized}, author = {Kachhadiya, Aaditya L.}, journal = {arXiv preprint arXiv:2605.13068}, year = {2026}, archiveprefix = {arXiv}, primaryclass = {cs.LG}, }
NeurIPS 2025 ML4PS
Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion

Aaditya L. Kachhadiya

In NeurIPS 2025 Machine Learning for Physical Sciences Workshop, 2025

Abs Bib PDF Poster

Inverse problems in the physical sciences are often ill-conditioned in input space, making progress step-size sensitive. We propose the Deceptron, a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Training combines a supervised fit, forward–reverse consistency, a lightweight spectral penalty, a soft bias tie, and a Jacobian Composition Penalty (JCP) that encourages \(J_g(f(x))J_f(x) ≈I\)via JVP/VJP probes. At solve time, D-IPG (Deceptron Inverse-Preconditioned Gradient) takes a descent step in output space, pulls it back through \(g\), and projects under the same backtracking and stopping rules as baselines. On Heat-1D initial-condition recovery and a Damped Oscillator inverse problem, D-IPG reaches a fixed normalized tolerance with \(∼20\times\)fewer iterations on Heat and \(∼2\)–\(3\times\)fewer on Oscillator than projected gradient, competitive in iterations and cost with Gauss–Newton. Diagnostics show JCP reduces a measured composition error and tracks iteration gains. We also preview a single-scale 2D instantiation, DeceptronNet (v0), that learns few-step corrections under a strict fairness protocol and exhibits notably fast convergence.
@inproceedings{kachhadiya2025deceptron, title = {Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion}, author = {Kachhadiya, Aaditya L.}, booktitle = {NeurIPS 2025 Machine Learning for Physical Sciences Workshop}, year = {2025}, }