CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

Operator Learning for Continuous Spatial-Temporal Model with A Hybrid Optimization Scheme

Partial differential equations are often used in the spatial-temporal modeling of complex dynamical systems in many engineering applications. In this work, we build on the recent progress of operator learning and present a data-driven modeling framework that is continuous in both space and time. A key feature of the proposed model is the resolution-invariance with respect to both spatial and temporal discretizations. To improve the long-term performance of the calibrated model, we further propose a hybrid optimization scheme that leverages both gradient-based and derivative-free optimization methods and efficiently trains on both short-term time series and long-term statistics. We investigate the performance of the spatial-temporal continuous learning framework with three numerical examples, including the viscous Burgers' equation, the Navier-Stokes equations, and the Kuramoto-Sivashinsky equation. The results confirm the resolution-invariance of the proposed modeling framework and also demonstrate stable long-term simulations with only short-term time series data. In addition, we show that the proposed model can better predict long-term statistics via the hybrid optimization scheme with a combined use of short-term and long-term data.

CharacterChat: Learning towards Conversational AI with Personalized Social Support

In our modern, fast-paced, and interconnected world, the importance of mental well-being has grown into a matter of great urgency. However, traditional methods such as Emotional Support Conversations (ESC) face challenges in effectively addressing a diverse range of individual personalities. In response, we introduce the Social Support Conversation (S2Conv) framework. It comprises a series of support agents and the interpersonal matching mechanism, linking individuals with persona-compatible virtual supporters. Utilizing persona decomposition based on the MBTI (Myers-Briggs Type Indicator), we have created the MBTI-1024 Bank, a group that of virtual characters with distinct profiles. Through improved role-playing prompts with behavior preset and dynamic memory, we facilitate the development of the MBTI-S2Conv dataset, which contains conversations between the characters in the MBTI-1024 Bank. Building upon these foundations, we present CharacterChat, a comprehensive S2Conv system, which includes a conversational model driven by personas and memories, along with an interpersonal matching plugin model that dispatches the optimal supporters from the MBTI-1024 Bank for individuals with specific personas. Empirical results indicate the remarkable efficacy of CharacterChat in providing personalized social support and highlight the substantial advantages derived from interpersonal matching. The source code is available in \url{https://github.com/morecry/CharacterChat}.

CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting

Regime switching is ubiquitous in many complex dynamical systems with multiscale features, chaotic behavior, and extreme events. In this paper, a causation entropy boosting (CEBoosting) strategy is developed to facilitate the detection of regime switching and the discovery of the dynamics associated with the new regime via online model identification. The causation entropy, which can be efficiently calculated, provides a logic value of each candidate function in a pre-determined library. The reversal of one or a few such causation entropy indicators associated with the model calibrated for the current regime implies the detection of regime switching. Despite the short length of each batch formed by the sequential data, the accumulated value of causation entropy corresponding to a sequence of data batches leads to a robust indicator. With the detected rectification of the model structure, the subsequent parameter estimation becomes a quadratic optimization problem, which is solved using closed analytic formulae. Using the Lorenz 96 model, it is shown that the causation entropy indicator can be efficiently calculated, and the method applies to moderately large dimensional systems. The CEBoosting algorithm is also adaptive to the situation with partial observations. It is shown via a stochastic parameterized model that the CEBoosting strategy can be combined with data assimilation to identify regime switching triggered by the unobserved latent processes. In addition, the CEBoosting method is applied to a nonlinear paradigm model for topographic mean flow interaction, demonstrating the online detection of regime switching in the presence of strong intermittency and extreme events.