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Task-conditional architecture offers advantage in parameter efficiency but falls short in performance compared to state-of-the-art multi-decoder methods. How to trade off performance and model parameters is an important and difficult…

This paper proposes a latent prompt Transformer model for solving challenging optimization problems such as molecule design, where the goal is to find molecules with optimal values of a target chemical or biological property that can be…

A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based…

Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods…

Time series forecasting is essential for a wide range of real-world applications. Recent studies have shown the superiority of Transformer in dealing with such problems, especially long sequence time series input(LSTI) and long sequence…

We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…

We study boundary value problems for degenerate elliptic equations and systems with square integrable boundary data. We can allow for degeneracies in the form of an $A_{2}$ weight. We obtain representations and boundary traces for solutions…

Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…

In multivariate time series forecasting, the Transformer architecture encounters two significant challenges: effectively mining features from historical sequences and avoiding overfitting during the learning of temporal dependencies. To…

Time series forecasting is extensively applied across diverse domains. Transformer-based models demonstrate significant potential in modeling cross-time and cross-variable interaction. However, we notice that the cross-variable correlation…

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

Time series forecasting is important in many fields that require accurate predictions for decision-making. Patching techniques, commonly used and effective in time series modeling, help capture temporal dependencies by dividing the data…

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…

Transformers have demonstrated impressive strength in long-term series forecasting. Existing prediction research mostly focused on mapping past short sub-series (lookback window) to future series (forecast window). The longer training…

Effective trajectory generation is essential for reliable on-board spacecraft autonomy. Among other approaches, learning-based warm-starting represents an appealing paradigm for solving the trajectory generation problem, effectively…

Training deep learning models can be computationally expensive. Prior works have shown that increasing the batch size can potentially lead to better overall throughput. However, the batch size is frequently limited by the accelerator memory…

Spacecraft operations are influenced by uncertainties such as dynamics modeling, navigation, and maneuver execution errors. Although mission design has traditionally incorporated heuristic safety margins to mitigate the effect of…

We consider a mixed type boundary value problem for a class of degenerate parabolic-hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary…

Large-scale self-supervised pre-training Transformer architecture have significantly boosted the performance for various tasks in natural language processing (NLP) and computer vision (CV). However, there is a lack of researches on…