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In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
Despite the growing popularity of Multimodal Domain Generalization (MMDG) for enhancing model robustness, it remains unclear whether reported performance gains reflect genuine algorithmic progress or are artifacts of inconsistent evaluation…
We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly…
Data Assimilation is a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
As the number of novel data-driven approaches to material science continues to grow, it is crucial to perform consistent quality, reliability and applicability assessments of model performance. In this paper, we benchmark the Materials…
PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only understanding the mathematical structure of PDEs, but also…
Progress toward the United Nations Sustainable Development Goals (SDGs) has been hindered by a lack of data on key environmental and socioeconomic indicators, which historically have come from ground surveys with sparse temporal and spatial…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…
Discovering the governing equations of dynamical systems is a central problem across many scientific disciplines. As experimental data become increasingly available, automated equation discovery methods offer a promising data-driven…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
Model-based testing (MBT) provides an automated approach for finding discrepancies between software models and their implementation. If we want to incorporate MBT into the fast and iterative software development process that is Continuous…
We introduce DRBench, a benchmark for evaluating AI agents on complex, open-ended deep research tasks in enterprise settings. Unlike prior benchmarks that focus on simple questions or web-only queries, DRBench evaluates agents on multi-step…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…