Burgers-inverse Open-Source Model - Solving the Inverse Problem of the Burgers Equation, Predicting Velocity Evolution and Estimating Parameters

Burgers Inverse

Developed by piotrnobis

A deep learning model for solving the inverse problem of Burgers equation, capable of predicting velocity evolution and estimating physical parameters

Physics Model

TensorBoard

English#Fluid Mechanics Inversion #Physical Parameter Estimation #UNet2D-MLP Hybrid Architecture

Downloads 335

Release Time : 4/14/2024

Model Overview

This model focuses on solving the inverse problem of Burgers equation through deep learning, predicting velocity evolution based on initial conditions, estimating hidden physical parameters, and handling incomplete data.

Model Features

Initial Condition Prediction

Predicts the development of liquid velocity over time based on initial conditions

Physical Parameter Estimation

Estimates hidden physical parameters such as viscosity coefficient

Computational Efficiency

Uses deep learning to approximate and replace computationally expensive simulation processes

Incomplete Data Handling

Infers missing velocity fields through masked inputs to handle incomplete data

Model Capabilities

Velocity Field Prediction

Physical Parameter Regression

Incomplete Data Inference

Use Cases

Fluid Mechanics Simulation

Velocity Field Evolution Prediction

Predicts changes in liquid velocity field over time based on initial conditions

Viscosity Coefficient Estimation

Estimates the viscosity coefficient of a liquid from observed data

Computational Fluid Dynamics

Simulation Replacement

Replaces traditional computational fluid dynamics simulations to reduce computational costs

🚀 Burgers’ Equation Inverse Problem - Deep Learning Model

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

🚀 Quick Start

📌 Project Overview

This project is centered around solving the inverse problem of the Burgers’ equation with deep - learning techniques. The main objective is to estimate the velocity evolution of liquids based on initial conditions or physical parameters. Our model utilizes UNet2D for feature extraction and an MLP for parameter regression.

🚀 Application

After learning from simulated Burgers' equation data, the model can perform the following tasks:

🔄 Predict the 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 employs the Phiflow library to apply diffusion and advection processes, which evolve the velocity field over time. Diffusion smooths out field variations by spreading quantities over time, while advection is a backward technique that ensures stability even with large timesteps.

📚 Documentation

📊 Dataset Information

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

Dataset Splits

Split	Percentage	Description
Training	80%	Used for model learning
Validation	10%	For hyperparameter tuning
Test	10%	For model evaluation

Data Format

Each sample includes:

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

📦 Installation

Make sure the dependencies are installed:

pip install torch torchvision transformers

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