Engineering Papers⌕ Search

DOE OSTI · 1511248

Rejoinder

Abstract

We would like to thank all of the discussants for their thoughtful and insightful comments. We heartily agree with Willis Jensen’s remark that the collection of views from multiple different perspectives possible with a discussion paper has added greatly to the overall contribution. Roger Hoerl compactly and eloquently summarized our thoughts about the role of statisticians on teams: “to objectively lead a team of subject matter experts through the minefield of problem resolution.” We agree with Benjamin Slade that this leadership role can be achieved either through formally leading the team or by being an active, engaged member of the team with an eye on the overall goals of the team and impacting the structure of the decision-making process. Hoerl also highlights what solutions interdisciplinary teams should be seeking – namely those that are “the best business … or scientific solution[s], rather than the best statistical solutions.” If this is how we define the objective of the team’s problem-solving or decision-making efforts, then establishing ourselves as fully-included team members or even working towards leading the team efforts should become easier.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anderson-Cook, Christine Michaela, Lu, Lu, Parker, Peter A. 2019-01-02. Rejoinder. https://doi.org/10.1080/08982112.2018.1546396

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

TANTE: Time-adaptive operator learning via neural Taylor expansion

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.

97 MATHEMATICS AND COMPUTING↗

Structured illumination for surface-resolved grazing-incidence X-ray scattering

Grazing-incidence (GI) scattering techniques are widely used to characterize thin films, offering high surface sensitivity and insight into morphology and structure. However, these approaches typically provide statistical averaged information due to elongated footprint or limited spatial resolution due to beam size. Here we introduce a method that combines structured illumination with GI X-ray scattering and leverages our computational imaging approach to resolve local structural details. We demonstrate that our method captures local features of an organic semiconductor thin film without the need for sample rotation as in tomography. The method expands GI techniques from statistical averaging to high-resolution imaging, thereby providing the capability for detailed analysis of local material properties, such as domain shape, orientation and polymorphism, which are critical for advancing material design towards more efficient and tailored materials.

97 MATHEMATICS AND COMPUTING↗