Scientific Machine Learning: Emerging Topics: 42

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.