Ting Gao

Ting Gao, Jinqiao Duan, Xiaofan Li et al.

The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by differential-integral equations(i.e.,differential equations with non local terms) but with different exterior conditions. The non-Gaussianity of noises manifests as nonlocality at the level of mean exit time and escape probability. An objective of this paper is to make mean exit time and escape probability as efficient computational tools, to the applied probability community, for quantifying stochastic dynamics. An accurate numerical scheme is developed and validated for computing the mean exit time and escape probability. Asymptotic solution for the mean exit time is given when the pure jump measure in the Levy motion is small. From both the analytical and numerical results, it is observed that the mean exit time depends strongly on the domain size and the value of alpha in the alpha-stable Levy jump measure. The mean exit time can measure which of the two competing factors in alpha-stable Levy motion, i.e. the jump frequency or the jump size, is dominant in helping a process exit a bounded domain. The escape probability is shown to vary with the underlying vector field(i.e.,drift). The mean exit time and escape probability could become discontinuous at the boundary of the domain, when the process is subject to certain deterministic potential and the value of alpha is in (0,1).

Jin Guo, Ting Gao, Yufu Lan et al.

Stochastic Gumbel graph networks are proposed to learn high-dimensional time series, where the observed dimensions are often spatially correlated. To that end, the observed randomness and spatial-correlations are captured by learning the drift and diffusion terms of the stochastic differential equation with a Gumble matrix embedding, respectively. In particular, this novel framework enables us to investigate the implicit regularization effect of the noise terms in S-GGNs. We provide a theoretical guarantee for the proposed S-GGNs by deriving the difference between the two corresponding loss functions in a small neighborhood of weight. Then, we employ Kuramoto's model to generate data for comparing the spectral density from the Hessian Matrix of the two loss functions. Experimental results on real-world data, demonstrate that S-GGNs exhibit superior convergence, robustness, and generalization, compared with state-of-the-arts.

Huifang Huang, Ting Gao, Yi Gui et al.

Reinforcement learning (RL) is gaining attention by more and more researchers in quantitative finance as the agent-environment interaction framework is aligned with decision making process in many business problems. Most of the current financial applications using RL algorithms are based on model-free method, which still faces stability and adaptivity challenges. As lots of cutting-edge model-based reinforcement learning (MBRL) algorithms mature in applications such as video games or robotics, we design a new approach that leverages resistance and support (RS) level as regularization terms for action in MBRL, to improve the algorithm's efficiency and stability. From the experiment results, we can see RS level, as a market timing technique, enhances the performance of pure MBRL models in terms of various measurements and obtains better profit gain with less riskiness. Besides, our proposed method even resists big drop (less maximum drawdown) during COVID-19 pandemic period when the financial market got unpredictable crisis. Explanations on why control of resistance and support level can boost MBRL is also investigated through numerical experiments, such as loss of actor-critic network and prediction error of the transition dynamical model. It shows that RS indicators indeed help the MBRL algorithms to converge faster at early stage and obtain smaller critic loss as training episodes increase.

Lingyu Feng, Ting Gao, Wang Xiao et al.

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.

Lingyu Feng, Ting Gao, Min Dai et al.

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics.

Ting Gao, Stavros Orfanoudakis, Nan Lin et al.

Diffusion-based policies have gained significant popularity in Reinforcement Learning (RL) due to their ability to represent complex, non-Gaussian distributions. Stochastic Differential Equation (SDE)-based diffusion policies often rely on indirect entropy control due to the intractability of the exact entropy, while also suffering from computationally prohibitive policy gradients through the iterative denoising chain. To overcome these issues, we propose Flow Matching Policy with Entropy Regularization (FMER), an Ordinary Differential Equation (ODE)-based online RL framework. FMER parameterizes the policy via flow matching and samples actions along a straight probability path, motivated by optimal transport. FMER leverages the model's generative nature to construct an advantage-weighted target velocity field from a candidate set, steering policy updates toward high-value regions. By deriving a tractable entropy objective, FMER enables principled maximum-entropy optimization for enhanced exploration. Experiments on sparse multi-goal FrankaKitchen benchmarks demonstrate that FMER outperforms state-of-the-art methods, while remaining competitive on standard MuJoco benchmarks. Moreover, FMER reduces training time by 7x compared to heavy diffusion baselines (QVPO) and 10-15% relative to efficient variants.

Luxuan Yang, Ting Gao, Wei Wei et al.

Time series classification faces two unavoidable problems. One is partial feature information and the other is poor label quality, which may affect model performance. To address the above issues, we create a label correction method to time series data with meta-learning under a multi-task framework. There are three main contributions. First, we train the label correction model with a two-branch neural network in the outer loop. While in the model-agnostic inner loop, we use pre-existing classification models in a multi-task way and jointly update the meta-knowledge so as to help us achieve adaptive labeling on complex time series. Second, we devise new data visualization methods for both image patterns of the historical data and data in the prediction horizon. Finally, we test our method with various financial datasets, including XOM, S\&P500, and SZ50. Results show that our method is more effective and accurate than some existing label correction techniques.

Peng Zhang, Ting Gao, Jin Guo et al.

Early warning for epilepsy patients is crucial for their safety and well-being, in particular to prevent or minimize the severity of seizures. Through the patients' EEG data, we propose a meta learning framework to improve the prediction of early ictal signals. The proposed bi-level optimization framework can help automatically label noisy data at the early ictal stage, as well as optimize the training accuracy of the backbone model. To validate our approach, we conduct a series of experiments to predict seizure onset in various long-term windows, with LSTM and ResNet implemented as the baseline models. Our study demonstrates that not only the ictal prediction accuracy obtained by meta learning is significantly improved, but also the resulting model captures some intrinsic patterns of the noisy data that a single backbone model could not learn. As a result, the predicted probability generated by the meta network serves as a highly effective early warning indicator.

Chunhai Jiao, Jin Guo, Haoyan Zhang et al.

We study the problem of detecting the onset of path splitting in stochastic interpolation between probability distributions. This question is especially subtle when the target distribution is nonconvex or supported on disconnected components, where interpolating trajectories may separate into distinct branches. Motivated by the stochastic control and Schrödinger bridge viewpoint, we propose a Jacobi field based indicator for identifying candidate splitting times and locations. Our approach is based on the Jacobi field associated with the linearization of an induced interpolating flow. Starting from a stochastic interpolation ansatz, we construct an Eulerian velocity field by conditional averaging and derive its spatial Jacobian in terms of the local posterior geometry of the target sample cloud. This allows us to interpret the symmetric part of the Jacobian as a local strain tensor and to use its spectral structure to quantify the amplification of infinitesimal perturbations along reference trajectories. Numerical experiments on non-convex and disconnected target distributions show that the proposed indicator consistently localizes the emergence of branching regions and captures the temporal development of splitting. These results suggest that Jacobi field analysis provides a natural mathematical framework for studying local instability and splitting phenomena in stochastic interpolation.

Longfei Guo, Pengbo Li, Ting Gao et al.

With the rapid advancement of AI technology, we have seen more and more concerns on data privacy, leading to some cutting-edge research on machine learning with encrypted computation. Fully Homomorphic Encryption (FHE) is a crucial technology for privacy-preserving computation, while it struggles with continuous non-polynomial functions, as it operates on discrete integers and supports only addition and multiplication. Spiking Neural Networks (SNNs), which use discrete spike signals, naturally complement FHE's characteristics. In this paper, we introduce FHE-DiCSNN, a framework built on the TFHE scheme, utilizing the discrete nature of SNNs for secure and efficient computations. By leveraging bootstrapping techniques, we successfully implement Leaky Integrate-and-Fire (LIF) neuron models on ciphertexts, allowing SNNs of arbitrary depth. Our framework is adaptable to other spiking neuron models, offering a novel approach to homomorphic evaluation of SNNs. Additionally, we integrate convolutional methods inspired by CNNs to enhance accuracy and reduce the simulation time associated with random encoding. Parallel computation techniques further accelerate bootstrapping operations. Experimental results on the MNIST and FashionMNIST datasets validate the effectiveness of FHE-DiCSNN, with a loss of less than 3\% compared to plaintext, respectively, and computation times of under 1 second per prediction. We also apply the model into real medical image classification problems and analyze the parameter optimization and selection.

Yixin Wang, Ting Gao, Jinqiao Duan

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order relations into one metric, its global scalar distance can obscure transient, localized structural reorganizations during dynamic phase transitions. To overcome this limitation, we present a hierarchical dynamic evaluation framework driven by a novel topological and hypergraph reconstruction strategy. Instead of directly interpolating abstract network parameters, our method interpolates the underlying spatial geometry and rigorously recomputes the valid topological structures, ensuring physical fidelity. Along this geodesic, we introduce a set of multi-scale indicators: macroscopic metrics (Topological Distortion and Persistence Entropy) to capture global shifts, and a novel mesoscopic dual-perspective Hypergraph Entropy (node-perspective and edge-perspective) to detect highly sensitive, asynchronous local rewirings. We further propagate the cycle-level entropy change onto individual vertices to form a point-level topological field. Extensive evaluations on physical dynamical systems (Rayleigh-Van der Pol limit cycles, Double-Well cluster fusion), high-dimensional biological aggregation (D'Orsogna model), and longitudinal stroke fMRI data demonstrate the utility of combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.

Xiaoai Xu, Yixuan Zhou, Xiang Zhou et al.

Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate early-warning tasks. This study proposes a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling. Through systematic comparison, six methods including diffusion maps (DM) are selected to construct low-dimensional representations. Based on these, a data-driven stochastic differential equation model is established to robustly estimate the probability evolution scoring function of the system. Building on this, a new Score Function (SF) indicator is defined by incorporating Schrödinger bridge theory to quantify the likelihood of significant state transitions in the system. Experiments demonstrate that this indicator exhibits higher sensitivity and robustness in epilepsy prediction, enables earlier identification of critical points, and clearly captures dynamic features across various stages before and after seizure onset. This work provides a systematic theoretical framework and practical methodology for extracting early-warning signals from high-dimensional data.

Hanyu Pei, Jing-Xiao Liao, Qibin Zhao et al.

Drawing inspiration from our human brain that designs different neurons for different tasks, recent advances in deep learning have explored modifying a network's neurons to develop so-called task-driven neurons. Prototyping task-driven neurons (referred to as NeuronSeek) employs symbolic regression (SR) to discover the optimal neuron formulation and construct a network from these optimized neurons. Along this direction, this work replaces symbolic regression with tensor decomposition (TD) to discover optimal neuronal formulations, offering enhanced stability and faster convergence. Furthermore, we establish theoretical guarantees that modifying the aggregation functions with common activation functions can empower a network with a fixed number of parameters to approximate any continuous function with an arbitrarily small error, providing a rigorous mathematical foundation for the NeuronSeek framework. Extensive empirical evaluations demonstrate that our NeuronSeek-TD framework not only achieves superior stability, but also is competitive relative to the state-of-the-art models across diverse benchmarks. The code is available at https://github.com/HanyuPei22/NeuronSeek.

Ting Gao, Rodrigo Kappes Marques, Lei Yu

Traffic forecasting is an important application of spatiotemporal series prediction. Among different methods, graph neural networks have achieved so far the most promising results, learning relations between graph nodes then becomes a crucial task. However, improvement space is very limited when these relations are learned in a node-to-node manner. The challenge stems from (1) obscure temporal dependencies between different stations, (2) difficulties in defining variables beyond the node level, and (3) no ready-made method to validate the learned relations. To confront these challenges, we define legitimate traffic causal variables to discover the causal relation inside the traffic network, which is carefully checked with statistic tools and case analysis. We then present a novel model named Graph Spatial-Temporal Network Based on Causal Insight (GT-CausIn), where prior learned causal information is integrated with graph diffusion layers and temporal convolutional network (TCN) layers. Experiments are carried out on two real-world traffic datasets: PEMS-BAY and METR-LA, which show that GT-CausIn significantly outperforms the state-of-the-art models on mid-term and long-term prediction.

Ming Li, Ting Gao, Jingqiao Dua

Controlling the high-dimensional neural dynamics during epileptic seizures remains a significant challenge due to the nonlinear characteristics and complex connectivity of the brain. In this paper, we propose a novel framework, namely Graph-Regularized Koopman Mean-Field Game (GK-MFG), which integrates Reservoir Computing (RC) for Koopman operator approximation with Alternating Population and Agent Control Network (APAC-Net) for solving distributional control problems. By embedding Electroencephalogram (EEG) dynamics into a linear latent space and imposing graph Laplacian constraints derived from the Phase Locking Value (PLV), our method achieves robust seizure suppression while respecting the functional topological structure of the brain.

Ting Gao, Elvin Isufi, Winnie Daamen et al.

Estimating queue lengths at signalized intersections remains a challenge in traffic management, especially under partially observed conditions where vehicle flows are not fully captured. This paper introduces Q-Net, a data-efficient and interpretable framework for queue length estimation that performs robustly even when traffic conservation assumptions are violated. Q-Net integrates two widely available and privacy-friendly data sources: (i) vehicle counts from loop detectors near stop lines, and (ii) aggregated floating car data (aFCD), which divides each road section into segments and provides segment-wise average speed measurements. These data sources often differ in spatial and temporal resolution, creating fusion challenges. Q-Net addresses this by employing a tailored state-space model and an AI-augmented Kalman filter, KalmanNet, which learns the Kalman gain from data without requiring prior knowledge of noise covariances or full system dynamics. We build on the vanilla KalmanNet pipeline to decouple measurement dimensionality from section length, enabling spatial transferability across road segments. Unlike black-box models, Q-Net maintains physical interpretability, with internal variables linked to real-world traffic dynamics. Evaluations on main roads in Rotterdam, the Netherlands, demonstrate that Q-Net outperforms baseline methods by over 60\% in Root Mean Square Error (RMSE), accurately tracking queue formation and dissipation while correcting aFCD-induced delays. Q-Net also demonstrates strong spatial and temporal transferability, enabling deployment without costly sensing infrastructure like cameras or radar. Additionally, we propose a real-time variant of Q-Net, highlighting its potential for integration into dynamic, queue-based traffic control systems.

Songtao Li, Zhenyu Liao, Tianqi Hou et al.

Few-shot generation, the synthesis of high-quality and diverse samples from limited training data, remains a significant challenge in generative modeling. Existing methods trained from scratch often fail to overcome overfitting and mode collapse, and fine-tuning large models can inherit biases while neglecting the crucial geometric structure of the latent space. To address these limitations, we introduce Latent Iterative Refinement Flow (LIRF), a novel approach that reframes few-shot generation as the progressive densification of geometrically structured manifold. LIRF establishes a stable latent space using an autoencoder trained with our novel \textbf{manifold-preservation loss} $L_{\text{manifold}}$. This loss ensures that the latent space maintains the geometric and semantic correspondence of the input data. Building on this, we propose an iterative generate-correct-augment cycle. Within this cycle, candidate samples are refined by a geometric \textbf{correction operator}, a provably contractive mapping that pulls samples toward the data manifold while preserving diversity. We also provide the \textbf{Convergence Theorem} demonstrating a predictable decrease in Hausdorff distance between generated and true data manifold. We also demonstrate the framework's scalability by generating coherent, high-resolution images on AFHQ-Cat. Ablation studies confirm that both the manifold-preserving latent space and the contractive correction mechanism are critical components of this success. Ultimately, LIRF provides a solution for data-scarce generative modeling that is not only theoretically grounded but also highly effective in practice.

Wei Wei, Ting Gao, Jinqiao Duan et al.

Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian Lévy noise. Among these complex phenomena, the most likely transition paths between metastable states are important since these rare events may have a high impact in certain scenarios. Based on the large deviation principle, the most likely transition path could be treated as the minimizer of the rate function upon paths that connect two points. One of the challenges to calculate the most likely transition path for stochastic dynamical systems under non-Gaussian Lévy noise is that the associated rate function can not be explicitly expressed by paths. For this reason, we formulate an optimal control problem to obtain the optimal state as the most likely transition path. We then develop a neural network method to solve this issue. Several experiments are investigated for both Gaussian and non-Gaussian cases.

Cheng Fang, Yubin Lu, Ting Gao et al.

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, lots of log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios which could have high error and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by $α$-stable Lévy noise from only random pairwise data. Our innovations include: (1) designing a deep learning approach to learn both drift and diffusion coefficients for Lévy induced noise with $α$ across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, (3) proposing an end-to-end complete framework for stochastic systems identification under a general input data assumption, that is, $α$-stable random variable. Finally, numerical experiments and comparisons with the non-local Kramers-Moyal formulas with moment generating function confirm the effectiveness of our method.

Luxuan Yang, Ting Gao, Yubin Lu et al.

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions are, first, we propose a model called Lévy induced stochastic differential equation network, which explores compounded stochastic differential equations with $α$-stable Lévy motion to model complex time series data and solve the problem through neural network approximation. Second, we theoretically prove that the numerical solution through our algorithm converges in probability to the solution of corresponding stochastic differential equation, without curse of dimensionality. Finally, we illustrate our method by applying it to real financial time series data and find the accuracy increases through the use of non-Gaussian Lévy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of Lévy motion and the prediction lengths.

Yubin Lu, Romit Maulik, Ting Gao et al.

In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced by integrating local or nonlocal Fokker-Planck equations). We analyze this evolution through machine learning assisted construction of a time-dependent mapping that takes a reference distribution (say, a Gaussian) to each and every instance of our evolving distribution. If the reference distribution is the initial condition of a Fokker-Planck equation, what we learn is the time-T map of the corresponding solution. Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time. We demonstrate that this approach can approximate probability density function evolutions in time from observed sampled data for systems driven by both Brownian and Lévy noise. We present examples with two- and three-dimensional, uni- and multimodal distributions to validate the method.