Research Concept · 2026

When Physics
Teaches Vision

Four ways Differential Equations can make neural networks smarter, from smoothing features to adaptive depth.

Explore Architecture
The Core Idea

Physics-inspired
Deep Learning

Standard CNNs are powerful but arbitrary. What if we borrow rules from physics, equations that describe how heat spreads, how fluids flow, and plug them directly into the learning pipeline?


This work tests four distinct touchpoints where Differential Equations can interact with a ResNet-18 baseline. Each one is an ablation. Together, they tell a richer story than any single trick could.

ResNet ↔ ODE Connection
xn+1 = xn + f(xn)
ResNet residual block
dx/dt = f(x,t)
Continuous ODE form

A ResNet layer is literally a discrete Euler step of an ODE. This connection is the foundation of the entire project.

System Architecture

The Full Pipeline

System Architecture
The Full Pipeline
INPUT
32 × 32 px
Raw image fed into the network. Pixels are normalized, no processing yet.
CNN
ResNet-18
Convolutional layers extract edges, textures and shapes. Feature maps are rich but noisy.
PDE LAYER
Diffusion
∂u/∂t = κ ∇²u
Laplacian filter diffuses feature maps. Noise smoothed, structure preserved.
ATTENTION
PDE-smoothed
α = softmax(PDE(QKᵀ))
Attention map diffused before weighting. Focus spreads continuously, not spiky.
ODE BLOCK
Adaptive depth
dz/dt = f(z,t)
ODE solver replaces fixed layers. Easy images: fewer steps. Hard images: more steps.
CLASSIFIER
Softmax
Global average pooling → fully connected → softmax. Multi-class output.
DE component
Standard layer
∂u/∂t = κ ∇²u  ·  DiffusifyNet
Research Questions

Four Clear Objectives

01

Does PDE smoothing improve classification?

Test whether diffusion-based feature smoothing gives a baseline ResNet-18 measurably better accuracy.

02

Can PDE refine attention maps?

Visualize and quantify the difference between sharp, standard attention vs. PDE-smoothed attention across image classes.

03

Does anisotropic augmentation add robustness?

Measure accuracy under noise and blur perturbations with and without PDE-driven training augmentation.

04

Can ODE blocks match fixed layers?

Compare accuracy vs. NFEs (neural function evaluations) between a standard ResNet block and its ODE replacement.

Get In Touch

Contact

Interested in this research? Reach out

Email