🌀 Burgers’ Equation Inverse Problem - Deep Learning Model

📌 Project Overview

This project focuses on solving the inverse problem of the Burgers’ equation using deep learning. The goal of this project is to estimate the velocity evolution of liquids given either the initial conditions or the underlying physical parameters. Our model leverages UNet2D for feature extraction and an MLP for parameter regression.

🚀 Application

By learning from simulated Burgers' equation data, the model can:

🔄 Predict velocity development over time from initial conditions.
🔍 Estimate hidden physical parameters (e.g., viscosity)
⚡ Replace computationally expensive simulations with a deep learning-based approximation.
🧩 Handle incomplete data by using masked inputs to infer missing velocity fields.

Run the simulation

The project is using Phiflow library to apply diffusion and advection processes - evolve the velocity field over time. Diffusion smooths out variations in the field by spreading the quantities over time, where as advection is a backward technique ensuring stability even with large timesteps.

📊 Dataset Information

The dataset consists of simulated velocity fields and their corresponding physical parameters.

Dataset Splits

Split	Percentage	Description
Training	80%	Used for model learning
Validation	10%	Hyperparameter tuning
Test	10%	Model evaluation

Data Format

Each sample consists of:

Input: 2D velocity field ( u(x,t) ) (tensor format).
Output: Corresponding physical parameters (e.g., viscosity ( \nu )).

⚙️ Model Usage

Installation

Ensure dependencies are installed:

pip install torch torchvision transformers