arXiv subjects

Souvik Chakraborty

Publications and source records attributed to Souvik Chakraborty.

3 recordsLinked to original sources

arXiv2026

See, Hypothesize, Validate: Multimodal Agentic Framework for Discovering Governing PDEs

Discovering governing partial differential equations (PDEs) from observational data remains a core challenge across the sciences. Existing sparse-regression, symbolic-regression, and LLM-based approaches can be constrained by predefined libraries, noise sensitivity, hallucination, or limited iterative refinement. We introduce \textbf{MAGE} (\textbf{M}ultimodal \textbf{A}gentic \textbf{G}overning \textbf{E}quation Discovery), an agentic framework that organizes PDE discovery as a \textit{confidence governed hypothesis validation loop} inspired by the scientific cycle of observation, hypothesis, and falsification. Four role-specialized agents collaborate: a \textit{Differential Observer} computing derivatives and diagnostic visualizations; a VLM-powered \textit{Phenomenology Extractor} distilling qualitative cues from multimodal diagnostics; an LLM-driven \textit{Governing Law Synthesizer} proposing candidates without a predefined library; and an \textit{Equation Arbiter} fitting coefficients and assigning confidence scores. Discovery iterates until the top candidate clears a user-specified threshold, providing a structured process with an explicit accept-reject protocol. On the evaluated canonical PDE suite, MAGE obtains \textbf{8/8} exact structural recovery and the lowest coefficient error among the compared methods on \textbf{7/8} systems, with improvements of up to \textbf{4 orders of magnitude} and a geometric-mean improvement of approximately \textbf{3 orders of magnitude}. The pipeline also recovers the expected operators in two complex geometries and, on one laboratory sensor record, selects a cubic restoring-force model with held-out $R^2=0.98538$. These results support further study of structured agentic reasoning for library-free governing-law discovery, while broader generalization remains to be evaluated.

cs.AI↗

arXiv2026

Beyond Pairwise Graphs in Science: Hypergraph Adaptive Wavelet Operators for Parametric PDEs

Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical states. Learning these maps is difficult, especially for time-dependent systems that must assimilate history and remain stable under autoregressive rollout. Many neural operators work best on regular, structured grids, while realistic simulations often require unstructured meshes or point clouds to resolve complex geometries; in such settings, grid-centric representations can lose accuracy. Graph neural operators handle these domains through message passing or spectral graph filtering, but pairwise edges do not directly capture group-wise couplings among mesh cells, local neighborhoods, or conservation volumes. We introduce the Hypergraph Adaptive waveLet Operator (HALO), which lifts the domain to a hypergraph and learns in its spectral wavelet domain. HALO avoids explicit hypergraph-Laplacian eigendecomposition through Chebyshev polynomial wavelet filters, giving localized spectral kernels at linear sparse-matrix cost. Its trainable dyadic wavelet scales are regularized toward tight-frame coverage, allowing the frequency response to adapt to each PDE while encouraging stable multi-scale spectral coverage. Across 2D and 3D benchmarks on structured and unstructured discretizations, HALO achieves best or near-best accuracy among frequency-, transformer-, DeepONet-, state-space-, and graph-based baselines and sustains stable multi-step rollouts. The same model scales to industrial aerodynamic geometries: on meshes of a few hundred thousand points it is on par with, or better than, the strongest fixed-discretization transformers, while remaining resolution-equivariant.

cs.LG↗

arXiv2026

Hardware-Software Co-Design for Event-Driven SNN Deployment on Low-Cost Neuromorphic FPGAs

Low-cost FPGA platforms can broaden access to neuromorphic systems research, but current spiking neural network (SNN) workflows remain divided between hardware-first implementations, which are difficult to integrate with PyTorch-style development, and software-first frameworks, which often stop at simulation or GPU execution. This paper presents a semantics-preserving hardware-software co-design framework for the deterministic deployment of PyTorch-defined SNNs to event-driven FPGA execution. A single exported artifact carries weights, thresholds, connectivity descriptors, and grouped time-to-first-spike (TTFS) decoding metadata from software definition to board execution and is reused unchanged by both the software reference and the board runtime. A 10-class MNIST TTFS classifier implemented in the routed 80 MHz design achieves 87.40% accuracy and matches the software reference on all 10,000 test images. The programmable-logic path delivers a service latency of 0.1375 μs/image and an estimated dynamic energy of 31.6 nJ/image, while scope-aware comparisons with matched GPU and CPU baselines keep accelerator-only and system-level measurements distinct. These results show that low-cost event-driven FPGA hardware can provide a direct and reproducible software-to-board path for software-defined SNN models.

cs.AR↗