Combating air pollution has proven to be a difficult task for countries with rapidly developing economies. Poor air quality can be hazardous to people doing any outdoor activities. So being able to make accurate, short term air quality predictions can be very useful. However, making these predictions has proven to be quite difficult, since there are a lot of different physical and chemical processes involved in the emission and transport of the various aerosols that contribute to air pollution. So instead of the more traditional Chemical Transport Models (CTMs) we will be using neural networks in order to make predictions of one of these aerosols, PM2.5. In particular, we will be using a Long Short Term Memory (LSTM) network. In addition, we will include the simulations results from a CTM, LOTOS-EUROS, as input data to the LSTM network to improve the performance of the neural network. One of the main drawbacks of the LSTM approach is that whenever the PM2.5 concentration changes a lot, the predictions made by the LSTM network take some time to change as well, causing a visible time delay when looking at the measurements and predictions in the same time series plot. We will also try a simpler type of neural network, a Feedforward Neural Network (FNN) and compare its performance to that of LSTM. We found that using the simulation data does indeed improve the LSTM network. Not only in terms of the loss function used by the neural network and, but in particular in the amount gross overestimations by the network, which we use to quantify the LSTM time delay problem. We also found that FNN outperforms the LSTM approach, in particular on samples of high PM2.5 concentrations, which we argue is primarily caused by a low amount of samples in our dataset.

In this thesis, we model the diusion of a tracer polymer inside of a gel network and simulate it, hoping to nd a connection between the diusion of the polymer and the strength of the gel network. This model is made by using the Rouse model for the gel network and the tracer polymer.
The overdamped Langevin equation is then used to nd a set of coupled stochastic dierential equations for the motion of a single tracer bead and the Fourier modes of the gel particles. The single particle system is then analyzed using three dierent numerical methods: The Euler forward method, the Metropolis Monte Carlo method and the Gillespie algorithm. The Gillespie algorithm is then used to expand the single particle model to a model which again includes a tracer polymer instead of a single tracer bead. The simulations of the tracer polymer suggest that the motion of the tracer polymer is superdiusive. This contradicts the theory and the measurements of the single
tracer particle, which suggest that the simulation of the polymer should result in subdiusion. This contradiction seems to be caused by an error in the implementation of the interaction between the dierent beads that make up the tracer polymer, as it creates a tendency for the polymer to move away from its original position. This possible error is hinted at by a simulation of the system with the tracer polymer where the gel is considered stationary. The simulation implies superdiusion as well, which means that the superdiusion is not caused by the gel network. In fact, the simulation with the frozen gel network is much further away from subdiusion that the simulation with the gel network intact, which does seem to imply that the motion would be subdiusive if the model
was implemented correctly, but it is not conclusive.