<p>Optimisation and machine learning techniques are increasingly used with net-shape composites forming methods like resin transfer moulding (RTM) for process monitoring, control, and defect detection. However, the standard finite element-control volume modelling approach used in these simulations is discontinuous with respect to model parameters and time. We demonstrate that the use of a neural network surrogate, designed with smooth activation layers, can approximate these models, while eliminating any nonsmooth or discontinuous behaviour. To illustrate the benefits of this method, we use Bayesian inference to predict permeability and race tracking strengths from pressure measurements, where the neural network prevents discontinuities from propagating to the posterior, forming smooth posterior distributions that incorporate the model approximation error.</p>