Skip to main content



Heat equation inversion

The heat equation is another classic example of an inverse problem. The following example shows how you can estimate time dependent temperature distribution on a 1d domain using several point measurements when heating is localized to a few fixed points. This is done with the help of sparse matrices and regularized least squares. Regularization of the second derivative used used to ensure smoothness of the reconstructed heating.

A generalization of this to 2d and 3d (and with advection added to the model) has applications for example in oceanography, where the inverse problem is to estimate the methane release from localized sources in the sea floor.

#!/usr/bin/env python # # Inverse problems with the 1d heat equation # (c) 2017 Juha Vierinen # import numpy as n import matplotlib.pyplot as plt from scipy.sparse import coo_matrix import scipy.sparse.linalg as s import lsqlin def create_theory_matrix(n_t=200,n_x=200, dt=2.0,dx=1.0,C=0.5, …

Latest posts

Markov random field removal of stars and interference from auroral images

A Year of CO₂

Solar activity swallows HF radio signals

Visualization of convolution

Deconvolution in frequency domain with a few lines of Python code

Inverse problems course

Tyttebær (Lingonberries)

Pass the filter, please...

Recent solar activity picked up by KAIRA

Mystery of the Ionosphere’s “Gyro Line” Solved

Water On the Moon, Pt. 3

Happy 40th, Voyager!

Water On the Moon, Pt. 2

The Gustavsson Macroscopic Plasma Experiment

Make you own guitar effects using GNURadio Companion

Ionospheric effects of the 2017 US Solar eclipse observed using a global network of GNSS receivers

New PhD thesis on Lunar meteoric impact related electromagnetic pulses

EISCAT 3D demonstrator array

100 kW coaxial cables and coaxial switches at EISCAT heating