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Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains underexplored. Learning problems in physical systems are often characterized as discovering operators that map between function spaces based on a few instances of function pairs. This task frequently presents a severely ill-posed PDE inverse problem. In this work, we propose a novel neural operator architecture based on the attention mechanism, which we refer to as the Nonlocal Attention Operator (NAO), and explore its capability in developing a foundation physical model. In particular, we show that the attention mechanism is equivalent to a double integral operator that enables nonlocal interactions among spatial tokens, with a data-dependent kernel characterizing the inverse mapping from data to the hidden parameter field of the underlying operator. As such, the attention mechanism extracts global prior information from training data generated by multiple systems, and suggests the exploratory space in the form of a nonlinear kernel map. Consequently, NAO can address ill-posedness and rank deficiency in inverse PDE problems by encoding regularization and achieving generalizability. We empirically demonstrate the advantages of NAO over baseline neural models in terms of generalizability to unseen data resolutions and system states. Our work not only suggests a novel neural operator architecture for learning interpretable foundation models of physical systems, but also offers a new perspective towards understanding the attention mechanism. Our code and data accompanying this paper are available at https://github.com/fishmoon1234/NAO. 

Abstract Manipulating surface charge, electric field, and plasma afterglow in a non-equilibrium plasma is critical to control plasma-surface interaction for plasma catalysis and manufacturing. Here, we show enhancements of surface charge, electric field during breakdown, and afterglow by ferroelectric barrier discharge. The results show that the ferroelectrics manifest spontaneous electric polarization to increase the surface charge by two orders of magnitude compared to discharge with an alumina barrier. Time-resolved in-situ electric field measurements reveal that the fast polarization of ferroelectrics enhances the electric field during the breakdown in streamer discharge and doubles the electric field compared to the dielectric barrier discharge. Moreover, due to the existence of surface charge, the ferroelectric electrode extends the afterglow time and makes discharge sustained longer when alternating the external electric field polarity. The present results show that ferroelectric barrier discharge offers a promising technique to tune plasma properties for efficient plasma catalysis and electrified manufacturing. 

Abstract Systems thinking (ST) includes a set of critical skills and approaches for addressing today's complex societal problems. Therefore, it has been introduced into the curricula of many educational programmes around the world. Despite all the attention to ST, there is less consensus when it comes to evaluating and assessing ST skills. Particularly, a quantitative assessment approach that captures ST's multi‐dimensionality is crucial when evaluating the degree to which one has learned and utilizes ST. This paper proposes a systematic approach to create such a multi‐dimensional Index of ST from textual data. Initially, we provide an overview of the theoretical background as it pertains to different measurement approaches of ST skills. Then we provide a conceptual framework based on ST skill measures and transform this framework into a quantifiable model. Finally, using student data, we provide an illustration of an integrated index of ST skills. We compute this index by using a mixed methods approach, including robust principal component analysis, data envelopment analysis and two‐staged bootstrapping approach. The results show that (i) our model serves as a systematic multi‐dimensional ST approach by including multiple measures of ST skills and (ii) international students and self‐reported math skills are found as significant predictors of one's level of ST in the graduate student dataset (N = 30), however no significant factors are found in the first‐year engineering student dataset (N = 144).