Katarzyna Michałowska

Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis et al.

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data. Existing methods, however, cannot extrapolate accurately and are prone to error accumulation in long-time integration. Herein, we address this issue by combining neural operators with recurrent neural networks, learning the operator mapping, while offering a recurrent structure to capture temporal dependencies. The integrated framework is shown to stabilize the solution and reduce error accumulation for both interpolation and extrapolation of the Korteweg-de Vries equation.

Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis et al.

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. This property becomes especially relevant in real-world scenarios where high-resolution measurements are difficult to obtain, while low-resolution data is more readily available. Nevertheless, DeepONets alone often struggle to capture and maintain dependencies over long sequences compared to other state-of-the-art algorithms. We propose a novel architecture, named DON-LSTM, which extends the DeepONet with a long short-term memory network (LSTM). Combining these two architectures, we equip the network with explicit mechanisms to leverage multi-resolution data, as well as capture temporal dependencies in long sequences. We test our method on long-time-evolution modeling of multiple non-linear systems and show that the proposed multi-resolution DON-LSTM achieves significantly lower generalization error and requires fewer high-resolution samples compared to its vanilla counterparts.

Katarzyna Michałowska, Helga Margrete Bodahl Holmestad, Signe Riemer-Sørensen

We propose a new method for inferring roads from GPS trajectories to map construction sites. This task presents a unique challenge due to the erratic and non-standard movement patterns of construction machinery, which significantly diverge from typical vehicular traffic on established roads. Our proposed method first identifies intersections in the road network that serve as critical decision points, and then connects them with edges to produce a graph, which can subsequently be used for planning and task-allocation. We demonstrate the approach by mapping roads at a real-life construction site in Norway. The method is validated on four increasingly complex segments of the map. In our tests, the method achieved perfect accuracy in detecting intersections and inferring roads in data with no or low noise, while its performance was reduced in areas with significant noise and consistently missing GPS updates.