The paper presents heat release rate (HRR) inversion models for fires using heat fluxes, video footage, and temperatures as measurements. The models are trained on calibration experimental burner fires and evaluated for predicting transient HRR in excluded test experiments. A linear relationship between heat flux and HRR is leveraged for predictions. Regularization and lasso regression aid in feature selection and prediction. Temporally noisy predictions from linear regression are improved using Gaussian process regression (GPR). Similar approaches are applied using video footage and temperature measurements. The use of artificial neural networks (ANN) for HRR predictions in simulation models is explored, with transfer learning significantly reducing computational cost. Emulators based on ANNs produce accurate results at a fraction of the computational time. Bayesian parameter inversion for radiative fraction and ridge regression for weighted HRR estimation are presented, showing promise for HRR prediction.