Chuanqi Chen

Quan Tu, Chuanqi Chen, Jinpeng Li et al.

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}.

Chuanqi Chen, Nan Chen, Jin-Long Wu

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.

Xinghao Dong, Chuanqi Chen, Jin-Long Wu

Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a clear scale separation, deterministic and local closure models often lack enough generalization capability, which limits their performance in many real-world applications. In this work, we propose a data-driven modeling framework for constructing stochastic and non-local closure models via conditional diffusion model and neural operator. Specifically, the Fourier neural operator is incorporated into a score-based diffusion model, which serves as a data-driven stochastic closure model for complex dynamical systems governed by partial differential equations (PDEs). We also demonstrate how accelerated sampling methods can improve the efficiency of the data-driven stochastic closure model. The results show that the proposed methodology provides a systematic approach via generative machine learning techniques to construct data-driven stochastic closure models for multiscale dynamical systems with continuous spatiotemporal fields.

Chuanqi Chen, Jin-Long Wu

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different types of data, e.g., with different spatial and temporal resolutions, and the combined use of short-term trajectories and long-term statistics. In this work, we build on the recent progress of neural operator and present a data-driven modeling framework called neural dynamical operator that is continuous in both space and time. A key feature of the neural dynamical operator is the resolution-invariance with respect to both spatial and temporal discretizations, without demanding abundant training data in different temporal resolutions. 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 neural dynamical operator 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.

Zhongrui Wang, Chuanqi Chen, Jin-Long Wu et al.

Lagrangian data assimilation aims to recover hidden Eulerian flow fields from sparse, indirect observations of moving tracers. This problem is challenging because tracer trajectories are nonlinearly coupled with the underlying flow, making posterior inference computationally intractable in realistic, high-dimensional systems. In this work, we develop a Lagrangian conditional Gaussian Koopman network (LaCGKN), a structure-preserving, data-driven framework for joint data assimilation and prediction from Lagrangian observations. LaCGKN embeds Eulerian flow dynamics into a low-dimensional latent space governed by a nonlinear stochastic system with conditional Gaussian structure, enabling analytic posterior updates without ensemble forecasting. Unlike existing conditional Gaussian Koopman formulations that assume direct Eulerian observations, the Lagrangian setting imposes additional demands on the latent representation, which must simultaneously encode the flow dynamics and mediate nonlinear tracer-flow interactions. To address these challenges, the LaCGKN incorporates three key components: (i) tracer homogenization to enforce permutation equivariance and generalize across varying numbers of tracers; (ii) Fourier positional encoding to capture spatial dependence and reconstruct local flow features at moving tracer locations; and (iii) an SVD-inspired low-rank parameterization of the latent transition operator, which reduces model complexity while retaining expressiveness. An application to a two-layer quasi-geostrophic flow with surface tracer observations shows that LaCGKN achieves accurate and efficient Lagrangian data assimilation and prediction, without reliance on ensemble methods or the governing physical model. These results establish the LaCGKN as a unified and computationally tractable alternative to both traditional model-based approaches and purely black-box data-driven methods.

Chuanqi Chen, Nan Chen, Jin-Long Wu

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.

Chuanqi Chen, Nan Chen, Yinling Zhang et al.

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data assimilation (DA), which is a crucial technique for state estimation, model identification, and reconstructing missing data. Integrating ensemble-based DA methods with nonlinear deep learning models is computationally expensive and may suffer from large sampling errors. To address these challenges, we introduce a deep learning framework designed to simultaneously provide accurate forecasts and efficient DA. It is named Conditional Gaussian Koopman Network (CGKN), which transforms general nonlinear systems into nonlinear neural differential equations with conditional Gaussian structures. CGKN aims to retain essential nonlinear components while applying systematic and minimal simplifications to facilitate the development of analytic formulae for nonlinear DA. This allows for seamless integration of DA performance into the deep learning training process, eliminating the need for empirical tuning as required in ensemble methods. CGKN compensates for structural simplifications by lifting the dimension of the system, which is motivated by Koopman theory. Nevertheless, CGKN exploits special nonlinear dynamics within the lifted space. This enables the model to capture extreme events and strong non-Gaussian features in joint and marginal distributions with appropriate uncertainty quantification. We demonstrate the effectiveness of CGKN for both prediction and DA on three strongly nonlinear and non-Gaussian turbulent systems: the projected stochastic Burgers-Sivashinsky equation, the Lorenz 96 system, and the El Niño-Southern Oscillation. The results justify the robustness and computational efficiency of CGKN.

Huchen Yang, Chuanqi Chen, Jin-Long Wu

Digital twins have been actively explored in many engineering applications, such as manufacturing and autonomous systems. However, model discrepancy is ubiquitous in most digital twin models and has significant impacts on the performance of using those models. In recent years, data-driven modeling techniques have been demonstrated promising in characterizing the model discrepancy in existing models, while the training data for the learning of model discrepancy is often obtained in an empirical way and an active approach of gathering informative data can potentially benefit the learning of model discrepancy. On the other hand, Bayesian experimental design (BED) provides a systematic approach to gathering the most informative data, but its performance is often negatively impacted by the model discrepancy. In this work, we build on sequential BED and propose an efficient approach to iteratively learn the model discrepancy based on the data from the BED. The performance of the proposed method is validated by a classical numerical example governed by a convection-diffusion equation, for which full BED is still feasible. The proposed method is then further studied in the same numerical example with a high-dimensional model discrepancy, which serves as a demonstration for the scenarios where full BED is not practical anymore. An ensemble-based approximation of information gain is further utilized to assess the data informativeness and to enhance learning model discrepancy. The results show that the proposed method is efficient and robust to the active learning of high-dimensional model discrepancy, using data suggested by the sequential BED. We also demonstrate that the proposed method is compatible with both classical numerical solvers and modern auto-differentiable solvers.

Chuanqi Chen, Zhongrui Wang, Nan Chen et al.

A discrete-time conditional Gaussian Koopman network (CGKN) is developed in this work to learn surrogate models that can perform efficient state forecast and data assimilation (DA) for high-dimensional complex dynamical systems, e.g., systems governed by nonlinear partial differential equations (PDEs). Focusing on nonlinear partially observed systems that are common in many engineering and earth science applications, this work exploits Koopman embedding to discover a proper latent representation of the unobserved system states, such that the dynamics of the latent states are conditional linear, i.e., linear with the given observed system states. The modeled system of the observed and latent states then becomes a conditional Gaussian system, for which the posterior distribution of the latent states is Gaussian and can be efficiently evaluated via analytical formulae. The analytical formulae of DA facilitate the incorporation of DA performance into the learning process of the modeled system, which leads to a framework that unifies scientific machine learning (SciML) and data assimilation. The performance of discrete-time CGKN is demonstrated on several canonical problems governed by nonlinear PDEs with intermittency and turbulent features, including the viscous Burgers' equation, the Kuramoto-Sivashinsky equation, and the 2-D Navier-Stokes equations, with which we show that the discrete-time CGKN framework achieves comparable performance as the state-of-the-art SciML methods in state forecast and provides efficient and accurate DA results. The discrete-time CGKN framework also serves as an example to illustrate unifying the development of SciML models and their other outer-loop applications such as design optimization, inverse problems, and optimal control.