SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications

Shailesh Garg; Luis Mandl; Somdatta Goswami; Souvik Chakraborty

physics.comp-phMar 23, 2026

SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications

Authors: Shailesh Garg, Luis Mandl, Somdatta Goswami, Souvik Chakraborty

Organizations: Department of Applied Mechanics Indian Institute of Technology Delhi Hauz Khas, New Delhi 110016, India. · Institute of Structural Mechanics and Dynamics in Aerospace Engineering Faculty of Aerospace Engineering and Geodesy University of Stuttgart, Stuttgart, Germany. · Experimental Hepatobiliary Surgery Group Department of Hepatobiliary Surgery and Visceral Transplantation University of Leipzig Medical Center, Leipzig, Germany. · Department of Civil and Systems Engineering Johns Hopkins University, Maryland 21218, USA. ·

Abstract

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where repeated operator evaluations in dense networks incur substantial computational and energy costs. To address this challenge, we introduce the Separable Physics-informed Neuroscience-inspired Operator Network (SPINONet), a neuroscience-inspired framework that reduces redundant computation across repeated evaluations while remaining compatible with physics-informed training. SPINONet incorporates regression-friendly neuroscience-inspired spiking neurons through an architecture-aware design that enables sparse, event-driven computation, improving energy efficiency while preserving the continuous, coordinate-differentiable pathways required for computing spatio-temporal derivatives. We evaluate SPINONet on a range of partial differential equations representative of computational mechanics problems, with spatial, temporal, and parametric dependencies in both time-dependent and steady-state settings, and demonstrate predictive performance comparable to conventional physics-informed operator learning approaches despite the induced sparse communication. In addition, limited data supervision in a hybrid setup is shown to improve performance in challenging regimes where purely physics-informed training may converge to spurious solutions. Finally, we provide an analytical discussion linking architectural components and design choices of SPINONet to reductions in computational load and energy consumption.

Figures & tables

	Burgers	Heat (Parametric)	Eikonal
Spatial dimension	1D	2D	2D
Temporal dimension	1	1	–
Parameter	IC	$\alpha$ and IC	Geometry
Total dim., $d$	2	4	2
Branch hidden layers	$6\times 100$	$5\times 50$	$5\times 50$
Branch input size	101	1	400

Table 1: Summary of architectures, discretization, and training configurations for all numerical examples.

Equation	Model	$L^{2}$ error	Runtime (s)/Epoch	Spiking Activity
Burgers	PI-DeepONet	0.05	$\sim$ 0.604	-
	Vanilla Baseline	0.06	$\sim$ 0.012	-
	SPINONet	0.07	$\sim$ 0.013	53.41
Heat	PI-DeepONet	-	-	-
	Vanilla Baseline	0.10	$\sim$ 0.097	-
	SPINONet	0.09	$\sim$ 0.095	46.33

Table 2: Comparison of test

L^{2}

error and runtime per epoch for PI-DeepONet, Vanilla Baseline, and SPINONet across Burgers, Heat, and Eikonal equations. Average spiking activity averaged across all VSN layers of the branch net of SPINONet is also shown.

Figure 1: Mean per-layer spiking activity in the branch-network VSN layers across all numerical examples.

Panel of Figure 2 — Figure 2: Viscous Burgers equation: Representative comparisons between SPINONet and the vanilla baseline on unseen test samples. Rows correspond to different test cases, while columns show solution fields and error distributions.

Panel of Figure 3 — Figure 3: Viscous Burgers equation: Comparison of SPINONet and PI-DeepONet computational cost as a function of grid size. The top panel shows GPU memory consumption, and the bottom panel shows average training time per epoch. Error bars indicate one standard deviation computed over independent runs.

Figure 4: Heat equation with Parameteric Diffusion: SPINONet predictions at selected values of $\alpha$ . Shown are representative planar slices and volumetric renderings of $u(x,y,t)$ .

Figure 5: Heat equation with Parameteric Diffusion: Comparison of reference solutions, SPINONet predictions, vanilla baseline predictions, and absolute errors. Columns correspond to different test cases, while rows show solution fields and error distributions.

Figure 6: Eikonal equation with parametric boundaries: Comparison of reference solutions, SPINONet predictions, vanilla baseline predictions, and corresponding absolute errors. Rows correspond to test samples; columns show solution fields and absolute errors.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Eikonal equation with parametric boundaries: Representative degenerate convergence modes for the Eikonal equation using the vanilla baseline. Erroneous convergence and flipped-sign convergence, along with the corresponding absolute errors.

Figure 8: Eikonal equation with parametric boundaries: Comparison of true convergence and flipped-sign convergence for the Eikonal equation, with corresponding absolute errors, when using the proposed SPINONet.

Physics-Informed Neural Operators

Physics-informed neural operators learn mappings between physical fields while embedding governing equations or structural constraints for faster, more reliable simulation.

See all 72 papers

SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving
Apr 13, 2026Samrendra Roy, Souvik Chakraborty, Rizwan-uddin +1PDE Solving PDE Surrogate Modeling
University of Illinois Urbana-Champaign Department of Nuclear, Plasma & Radiological Engineering Urbana, IL, USA · Indian Institute of Technology Delhi Department of Applied Mechanics New Delhi, India · National Center for Supercomputing Applications Urbana, IL, USA
Preconditioned Physics-Informed Neural Operator Training
Sep 28, 2026Shizheng Wen, Siddhartha Mishra, Marius ZeinhoferPhysics-Informed Neural Operators PDE Operator Learning
ETH Zürich
On the training of physics-informed neural operators for solving parametric partial differential equations
Jun 4, 2026Nanxi Chen, Chuanjie Cui, Airong Chen +2Neural Network Optimization Gradient Interference
College of Civil Engineering, Tongji University, Shanghai 200092 · Department of Engineering Science, University of Oxford, Oxford OX1 3PJ · Institute for Foundations of Data Science, Yale University, New Haven, CT 06520

Apr 13, 2026J/K move · Enter open · S save

SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

Samrendra Roy, Souvik Chakraborty, Rizwan-uddin, Syed Bahauddin Alam

University of Illinois Urbana-Champaign Department of Nuclear, Plasma & Radiological Engineering Urbana, IL, USA · Indian Institute of Technology Delhi Department of Applied Mechanics New Delhi, India · National Center for Supercomputing Applications Urbana, IL, USA

PDE Solving PDE Surrogate Modeling Neural Operators Modular Neural Networks Neuromorphic Computing

Open paper AskPDF arXiv

Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking Compositional Neural Operator (SCNO), a modular architecture combining spiking and conventional components that addresses all three limitations. SCNO maintains a library of small spiking neural operator blocks, each trained on a single elementary differential operator (convection, diffusion, reaction), and composes them through a lightweight input-conditioned aggregator to solve coupled PDEs not seen during block training. A small correction network learns cross-coupling residuals while keeping all blocks and the aggregator frozen, preserving zero-forgetting modular expansion by construction. We evaluate SCNO on eight PDE families including five coupled systems and a nuclear-relevant 1-group neutron diffusion equation. SCNO with correction achieves the lowest relative

L^2

error on four of five coupled PDEs, outperforming both a monolithic spiking DeepONet (by up to 62%, mean over 3 seeds) and a standard ANN DeepONet (by up to 65%), while requiring only 95K trainable parameters versus 462K for the monolithic baseline. To our knowledge, this is the first compositional spiking neural operator and the first proof-of-concept for modular neuromorphic PDE solving with built-in forgetting-free expansion.

Abstract

Physics-Informed Neural Operators

Explore similar work

SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

Preconditioned Physics-Informed Neural Operator Training

On the training of physics-informed neural operators for solving parametric partial differential equations