商品描述
This volume gathers peer-reviewed papers from the workshop Scientific Machine Learning: Emerging Topics, held at SISSA in Trieste, Italy. The event gathered leading researchers in mathematics, algorithms, and machine learning. Its goal was to advance the synergy between data-driven models and scientific computing, promoting robust, interpretable, and scalable methods. The works reflect major trends in scientific machine learning (SciML), including optimization, physics-informed learning, neural graph/operators/ODE, transformers, and generative models. Contributions propose physics-based constrained neural networks, advancements in optimization and model reduction, and applications across power systems, chemical kinetics, and biomechanics. Topics span from hybrid models for image classification to generative compression and neural operators for high-dimensional systems. Blending theory and practice, the volume captures the diversity and innovation shaping modern SciML.
This volume is addressed to researchers and will provide readers with insight into the current state of the field, sparks new ideas, and encourages further research at the rich intersection of machine learning, mathematics, and scientific computing.
商品描述(中文翻譯)
本卷匯集了在義大利的特里斯特（Trieste）SISSA舉辦的研討會《科學機器學習：新興主題》的同行評審論文。此次活動聚集了數學、演算法和機器學習領域的領先研究者。其目標是促進數據驅動模型與科學計算之間的協同作用，推動穩健、可解釋且可擴展的方法。這些作品反映了科學機器學習（SciML）的主要趨勢，包括優化、物理知識驅動學習、神經圖/運算子/常微分方程（ODE）、變壓器（transformers）和生成模型。貢獻包括基於物理的約束神經網絡、優化和模型簡化的進展，以及在電力系統、化學動力學和生物力學等領域的應用。主題涵蓋從圖像分類的混合模型到生成壓縮和高維系統的神經運算子。這本卷結合了理論與實踐，捕捉了塑造現代SciML的多樣性和創新。
本卷針對研究人員，將為讀者提供對該領域當前狀態的洞察，激發新想法，並鼓勵在機器學習、數學和科學計算的豐富交集上進一步研究。
作者簡介
Federico Pichi received his Ph.D. in Mathematical Analysis, Modelling and Applications at SISSA, and he is currently an assistant professor in Numerical Analysis in the mathLab group at SISSA. His research interests include projection-based and data-driven reduced order models in computational science and engineering, with applications to parametrized bifurcating problems. He also develops scientific machine learning approaches bridging numerical analysis and novel architectures. Gianluigi Rozza is a professor in numerical analysis and scientific computing at International School for Advanced Studies-SISSA, Trieste, Italy. He obtained his Ph.D. in applied mathematics at EPFL in 2005, M.Sc. in aerospace engineering at Politecnico di Milano in 2002, and post-doc at MIT. At SISSA, he is a coordinator of the SISSA mathLab group and a lecturer in the master in high-performance computing. He is the SISSA director's delegate for Valorisation, Innovation, Technology Transfer, and Industrial Cooperation. His research is mostly focused on numerical analysis and scientific computing, developing reduced order methods. He is the author of more than 130 scientific publications (editor of six books and author of two books). He has been the advisor of 35 master theses and co-director/director of 22 Ph.D. theses since 2009. He is the principal investigator of the European Research Council Consolidator Grant (H2020) AROMA-CFD and PoC ARGOS (HE) as well as of the project FARE-AROMA-CFD funded by the Italian Government. Since 2022, he is the co-founder and scientific director of FAST Computing, a SISSA startup. Maria Strazzullo received her Ph.D. in Mathematical Analysis, Modelling and Applications at SISSA, and she is currently an assistant professor in Numerical Analysis at the Department of Mathematics of the Polytechnic of Turin. Her research focuses on reduced order models for parametric partial differential equations, with particular emphasis on optimal flow control and turbulence modeling, with the main goal of conceiving reliable and efficient methods for the simulation and control of complex systems. Davide Torlo received his Ph.D. in Mathematics at the University of Zurich, and he is currently assistant professor in Numerical Analysis at the Department of Mathematics of the University of Rome Sapienza. His interests lie chiefly in numerical methods for hyperbolic partial differential equations, including high order technique, structure preserving methods, and reduced order models. Lately, he also studied the applications of neural networks in this field.
作者簡介(中文翻譯)
Federico Pichi 於 SISSA 獲得數學分析、建模與應用的博士學位，目前是 SISSA mathLab 團隊的數值分析助理教授。他的研究興趣包括在計算科學和工程中基於投影和數據驅動的降維模型，並應用於參數化的分岔問題。他還開發科學機器學習方法，橋接數值分析和新穎架構。
Gianluigi Rozza 是義大利的國際高等研究學校 SISSA 的數值分析和科學計算教授。他於 2005 年在 EPFL 獲得應用數學博士學位，2002 年在米蘭理工大學獲得航空航天工程碩士學位，並在麻省理工學院完成博士後研究。在 SISSA，他是 SISSA mathLab 團隊的協調員，並在高效能計算碩士課程中擔任講師。他是 SISSA 校長在價值化、創新、技術轉移和產業合作方面的代表。他的研究主要集中在數值分析和科學計算，開發降維方法。他是超過 130 篇科學出版物的作者（編輯六本書和兩本書的作者）。自 2009 年以來，他已指導 35 篇碩士論文，並共同指導/指導 22 篇博士論文。他是歐洲研究委員會 Consolidator Grant (H2020) AROMA-CFD 和 PoC ARGOS (HE) 的主要研究者，以及由義大利政府資助的 FARE-AROMA-CFD 項目的主要研究者。自 2022 年以來，他是 SISSA 新創公司 FAST Computing 的共同創辦人和科學總監。
Maria Strazzullo 於 SISSA 獲得數學分析、建模與應用的博士學位，目前是都靈理工學院數學系的數值分析助理教授。她的研究專注於參數偏微分方程的降維模型，特別強調最佳流量控制和湍流建模，主要目標是設計可靠且高效的複雜系統模擬和控制方法。
Davide Torlo 於蘇黎世大學獲得數學博士學位，目前是羅馬薩賓納大學數學系的數值分析助理教授。他的興趣主要在於超雙曲偏微分方程的數值方法，包括高階技術、結構保持方法和降維模型。最近，他還研究了神經網絡在這一領域的應用。
