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This article introduces a novel numerical approach, based on finite-volume techniques, for studying fully nonlinear coagulation–fragmentation models, where both the coagulation and fragmentation components of the collision operator are nonlinear. The models come from three-wave kinetic equations, a pivotal framework in wave turbulence theory. Despite the importance of wave turbulence theory in physics and mechanics, there have been very few numerical schemes for three-wave kinetic equations, in which no additional assumptions are manually imposed on the evolution of the solutions, and the current manuscript provides one of the first of such schemes. To the best of our knowledge, this also is the first numerical scheme capable of accurately capturing the long-term asymptotic behaviour of solutions to a fully nonlinear coagulation–fragmentation model. The scheme is implemented on some test problems, demonstrating strong alignment with theoretical predictions of energy cascade rates, rigorously obtained in the work (Soffer & Tran. 2020Commun. Math. Phys.376, 2229–2276. (doi:10.1007/BF01419532)). We further introduce a weighted finite-volume variant to ensure energy conservation across varying degrees of kernel homogeneity. Convergence and first-order consistency are established through theoretical analysis and verified by experimental convergence orders in test cases. 

Individual variability of expressive behaviors is a major challenge for emotion recognition systems. Personalized emotion recognition strives to adapt machine learning models to individual behaviors, thereby enhancing emotion recognition performance and overcoming the limitations of generalized emotion recognition systems. However, existing datasets for audiovisual emotion recognition either have a very low number of data points per speaker or include a limited number of speakers. The scarcity of data significantly limits the development and assessment of personalized models, hindering their ability to effectively learn and adapt to individual expressive styles. This paper introduces EmoCeleb: a large-scale, weakly labeled emotion dataset generated via cross-modal labeling. EmoCeleb comprises over 150 hours of audiovisual content from approximately 1,500 speakers, with a median of 50 utterances per speaker. This rich dataset provides a rich resource for developing and benchmarking personalized emotion recognition methods, including those requiring substantial data per individual, such as set learning approaches. We also propose SetPeER: a novel personalized emotion recognition architecture employing set learning. SetPeER effectively captures individual expressive styles by learning representative speaker features from limited data, achieving strong performance with as few as eight utterances per speaker. By leveraging set learning, SetPeER overcomes the limitations of previous approaches that struggle to learn effectively from limited data per individual. Through extensive experiments on EmoCeleb and established benchmarks, i.e, MSP-Podcast and MSP-Improv, we demonstrate the effectiveness of our dataset and the superior performance of SetPeER compared to existing methods for emotion recognition. Our work paves the way for more robust and accurate personalized emotion recognition systems.