Browsing by Author "Ullrich, Finn"

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    Stochastic query synthesis for neural PDE solvers
    (2025) Ullrich, Finn
    PDEs are highly influential in physics and are describing various phenomena in the world, from wave movement to electro-magnetics. The problem arises when one tries to solve them, which requires enormous computing power for a numerical solution. To overcome the limitiations, neural PDE solvers have been proposed, using neural networks to approximate the solution trajectories. However, neural PDE solvers require training data from an computationally expensive numerical solver. Therefore, Musekamp et al. created a benchmark, which investigates active learning for neural PDE solvers. Active learning can reduce the amount of data required, while keeping the same performance. In this work, we will demonstrate a new strategy of selecting samples called stochastic query synthesis. Following this, we will remove the pool currently used and rather create a Markov chain directly from the input space containing unlabeled instances. The transition probability is based on the unadjusted Langevin algorithm, allowing us to sample by exploiting gradient information. To retrieve a better result, instead of just one chain, we will create multiple parallel chains, and only take the last state as input. We will show that this approach is equally effective as the currently implemented pool-based implementation. However, there are still performance problems that need to be solved in the future, to make it viable in practice.