Feel the Difference? A Comparative Analysis of Emotional Arcs in Real and LLM-Generated CBT Sessions

Synthetic therapy dialogues generated by large language models (LLMs) are increasingly used in mental health NLP to simulate counseling scenarios, train models, and supplement limited real-world data. However, it remains unclear whether these synthetic conversations capture the nuanced emotional dynamics of real therapy. In this work, we conduct the first comparative analysis of emotional arcs between real and LLM-generated Cognitive Behavioral Therapy dialogues. We adapt the Utterance Emotion Dynamics framework to analyze fine-grained affective trajectories across valence, arousal, and dominance dimensions. Our analysis spans both full dialogues and individual speaker roles (counselor and client), using real sessions transcribed from public videos and synthetic dialogues from the CACTUS dataset. We find that while synthetic dialogues are fluent and structurally coherent, they diverge from real conversations in key emotional properties: real sessions exhibit greater emotional variability,more emotion-laden language, and more authentic patterns of reactivity and regulation. Moreover, emotional arc similarity between real and synthetic speakers is low, especially for clients. These findings underscore the limitations of current LLM-generated therapy data and highlight the importance of emotional fidelity in mental health applications. We introduce RealCBT, a curated dataset of real CBT sessions, to support future research in this space.

Parameter Identification for Partial Differential Equations with Spatiotemporal Varying Coefficients

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the resolution of the parameter inverse problem from the observed spatiotemporal data a challenging endeavor. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural network, encompassing a sub-network, as our methodology for parameter identification, and a finite mixture model approach to detect regions of probable parameter variations. Through our scheme, we can precisely ascertain the unknown varying parameters of the complex multi-state system, thereby accomplishing the inversion of the varying parameters. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers' equation with time-varying parameters and the 2D wave equation with a space-varying parameter.