Shaofan Li

Qijun Chen, Shaofan Li

Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets. This mismatch can limit reconstruction accuracy, reduce sample quality, and constrain the expressive power of the learned latent space. We propose the eXact-Prior Variational Autoencoder (X-VAE), a framework that replaces the conventional standard normal prior with a Gaussian prior derived from the latent representations of a pretrained autoencoder (AE). Specifically, the empirical mean and standard deviation of the AE latent codes are used to parameterize a data-adaptive prior that more closely reflects the underlying structure of the training data. During generation, X-VAE introduces a latent scaling factor that enables explicit control over the variance of the sampled latent vectors, providing a simple mechanism for balancing sample diversity and fidelity. This flexibility makes the proposed approach particularly well suited for applications such as industrial and engineering design, where generated solutions must satisfy strict structural or functional constraints while still permitting meaningful design exploration. We present the mathematical formulation of well-suited X-VAE, derive the corresponding KL divergence objective for the proposed prior, and evaluate the method on standard benchmark datasets. Experimental results demonstrate that X-VAE preserves reconstruction quality while producing latent representations that better align with the empirical data distribution, leading to improved controllability and more realistic generated samples.

Xi Chen, Shaofan Li

The variational autoencoder (VAE) is a simple and efficient generative artificial intelligence method for modeling complex probability distributions of various types of data, such as images and texts. However, it suffers some main shortcomings, such as lack of interpretability in the latent variables, difficulties in tuning hyperparameters while training, producing blurry, unrealistic downstream outputs or loss of information due to how it calculates loss functions and recovers data distributions, overfitting, and origin gravity effect for small data sets, among other issues. These and other limitations have caused unsatisfactory generation effects for the data with complex distributions. In this work, we proposed and developed a polynomial hierarchical variational autoencoder (PH-VAE), in which we used a polynomial hierarchical date format to generate or to reconstruct the data distributions. In doing so, we also proposed a novel Polynomial Divergence in the loss function to replace or generalize the Kullback-Leibler (KL) divergence, which results in systematic and drastic improvements in both accuracy and reproducibility of the re-constructed distribution function as well as the quality of re-constructed data images while keeping the dataset size the same but capturing fine resolution of the data. Moreover, we showed that the proposed PH-VAE has some form of disentangled representation learning ability.

Qijun Chen, Shaofan Li

Due to climate change, the extreme wildfire has become one of the most dangerous natural hazards to human civilization. Even though, some wildfires may be initially caused by human activity, but the spread of wildfires is mainly determined by environmental factors, for examples, (1) weather conditions such as temperature, wind direction and intensity, and moisture levels; (2) the amount and types of dry vegetation in a local area, and (3) topographic or local terrian conditions, which affects how much rain an area gets and how fire dynamics will be constrained or faciliated. Thus, to accurately forecast wildfire occurrence has become one of most urgent and taunting environmental challenges in global scale. In this work, we developed a real-time Multimodal Transformer Neural Network Machine Learning model that combines several advanced artificial intelligence techniques and statistical methods to practically forecast the occurrence of wildfire at the precise location in real time, which not only utilizes large scale data information such as hourly weather forecasting data, but also takes into account small scale topographical data such as local terrain condition and local vegetation conditions collecting from Google Earth images to determine the probabilities of wildfire occurrence location at small scale as well as their timing synchronized with weather forecast information. By using the wildfire data in the United States from 1992 to 2015 to train the multimodal transformer neural network, it can predict the probabilities of wildfire occurrence according to the real-time weather forecast and the synchronized Google Earth image data to provide the wildfire occurrence probability in any small location ($100m^2$) within 24 hours ahead.

Xuan Hu, Qijun Chen, Nicholas H. Luo et al.

Peridynamics is a non-local continuum mechanics theory that offers unique advantages for modeling problems involving discontinuities and complex deformations. Within the peridynamic framework, various formulations exist, among which the material correspondence formulation stands out for its ability to directly incorporate traditional continuum material models, making it highly applicable to a range of engineering challenges. A notable advancement in this area is the bond-associated correspondence model, which not only resolves issues of material instability but also achieves high computational accuracy. However, the bond-associated model typically requires higher computational costs than FEA, which can limit its practical application. To address this computational challenge, we propose a novel surrogate model based on a message-passing neural network (MPNN) specifically designed for the bond-associated peridynamic material correspondence formulation. Leveraging the similarities between graph structure and the neighborhood connectivity inherent to peridynamics, we construct an MPNN that can transfers domain knowledge from peridynamics into a computational graph and shorten the computation time via GPU acceleration. Unlike conventional graph neural networks that focus on node features, our model emphasizes edge-based features, capturing the essential material point interactions in the formulation. A key advantage of this neural network approach is its flexibility: it does not require fixed neighborhood connectivity, making it adaptable across diverse configurations and scalable for complex systems. Furthermore, the model inherently possesses translational and rotational invariance, enabling it to maintain physical objectivity: a critical requirement for accurate mechanical modeling.

Chao Wang, Shaofan Li, Danielle Zeng et al.

In this paper, we introduce a probabilistic statistics solution or artificial intelligence (AI) approach to identify and quantify permanent (non-zero strain) continuum/material deformation only based on the scanned material data in the spatial configuration and the shape of the initial design configuration or the material configuration. The challenge of this problem is that we only know the scanned material data in the spatial configuration and the shape of the design configuration of three-dimensional (3D) printed products, whereas for a specific scanned material point we do not know its corresponding material coordinates in the initial or designed referential configuration, provided that we do not know the detailed information on actual physical deformation process. Different from physics-based modeling, the method developed here is a data-driven artificial intelligence method, which solves the problem with incomplete deformation data or with missing information of actual physical deformation process. We coined the method is an AI-based material deformation finding algorithm. This method has practical significance and important applications in finding and designing thermal compensation configuration of a 3D printed product in additive manufacturing, which is at the heart of the cutting edge 3D printing technology. In this paper, we demonstrate that the proposed AI continuum/material deformation finding approach can accurately find permanent thermal deformation configuration for a complex 3D printed structure component, and hence to identify the thermal compensation design configuration in order to minimizing the impact of temperature fluctuations on 3D printed structure components that are sensitive to changes of temperature.