Inverse modelling is a computational technique used to **estimate unknown parameters or states in a system based on observed data.** Unlike [[Forward modelling]], where known parameters are used to predict outcomes, inverse modelling starts with the outcomes and works backwards to find the possible parameters that could have led to those outcomes. Here are some key aspects: 1. **Parameter Estimation**: The primary aim is to find unknown parameters that could explain observed data. 2. **Data Fitting**: Inverse modeling often involves fitting a model to data, usually by minimizing the difference between the observed and predicted data. 3. **Optimization**: Techniques such as least squares, maximum likelihood, or Bayesian methods are often employed to find the best-fitting parameters. 4. **Ill-posed Problems**: Inverse modeling can sometimes result in problems that are "ill-posed," meaning they do not have a unique solution, are highly sensitive to input data, or both. 5. **Regularization**: To counteract ill-posedness, regularization techniques like adding constraints or penalties may be employed. 6. **Applications**: Widely used in various fields like seismology (Full Waveform Inversion), climate modeling, medical imaging (MRI, CT scans), and machine learning. 7. **Computational Intensity**: Often requires sophisticated computational techniques and high computational resources due to the complexity of the problem. 8. **Uncertainty**: Due to the nature of working with observed data, results often come with a measure of uncertainty. 9. **Validation**: Whenever possible, the results of inverse modeling are validated against independent data sets or through forward modeling. References: - ["Inverse Problem Theory and Methods for Model Parameter Estimation"](https://epubs.siam.org/doi/book/10.1137/1.9780898717921) - ["An Introduction to Inverse Problems with Applications"](https://link.springer.com/book/10.1007/978-3-642-39259-6)