Shupeng Wang

Nazanin Ahmadi Daryakenari, Shupeng Wang, George Karniadakis

In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug absorption, distribution, and their impact on targets. Although multi-compartment models are frequently utilized to elucidate intricate drug dynamics, they can also be overly complex. To generalize modeling while maintaining simplicity, we propose an innovative approach that enhances PK and integrated PK-PD modeling by incorporating fractional calculus or time-varying parameter(s), combined with constant or piecewise constant parameters. These approaches effectively model anomalous diffusion, thereby capturing drug trapping and escape rates in heterogeneous tissues, which is a prevalent phenomenon in drug dynamics. Furthermore, this method provides insight into the dynamics of drug in cancer in multi-dose administrations. Our methodology employs a Physics-Informed Neural Network (PINN) and fractional Physics-Informed Neural Networks (fPINNs), integrating ordinary differential equations (ODEs) with integer/fractional derivative order from compartmental modeling with neural networks. This integration optimizes parameter estimation for variables that are time-variant, constant, piecewise constant, or related to the fractional derivative order. The results demonstrate that this methodology offers a robust framework that not only markedly enhances the model's depiction of drug absorption rates and distributed delayed responses but also unlocks different drug-effect dynamics, providing new insights into absorption rates, anomalous diffusion, drug resistance, peristance and pharmacokinetic tolerance, all within a system of just two (fractional) ODEs with explainable results.

Binzong Geng, Min Yang, Fajie Yuan et al.

Lifelong learning capabilities are crucial for sentiment classifiers to process continuous streams of opinioned information on the Web. However, performing lifelong learning is non-trivial for deep neural networks as continually training of incrementally available information inevitably results in catastrophic forgetting or interference. In this paper, we propose a novel iterative network pruning with uncertainty regularization method for lifelong sentiment classification (IPRLS), which leverages the principles of network pruning and weight regularization. By performing network pruning with uncertainty regularization in an iterative manner, IPRLS can adapta single BERT model to work with continuously arriving data from multiple domains while avoiding catastrophic forgetting and interference. Specifically, we leverage an iterative pruning method to remove redundant parameters in large deep networks so that the freed-up space can then be employed to learn new tasks, tackling the catastrophic forgetting problem. Instead of keeping the old-tasks fixed when learning new tasks, we also use an uncertainty regularization based on the Bayesian online learning framework to constrain the update of old tasks weights in BERT, which enables positive backward transfer, i.e. learning new tasks improves performance on past tasks while protecting old knowledge from being lost. In addition, we propose a task-specific low-dimensional residual function in parallel to each layer of BERT, which makes IPRLS less prone to losing the knowledge saved in the base BERT network when learning a new task. Extensive experiments on 16 popular review corpora demonstrate that the proposed IPRLS method sig-nificantly outperforms the strong baselines for lifelong sentiment classification. For reproducibility, we submit the code and data at:https://github.com/siat-nlp/IPRLS.

Shuixin Fang, Shupeng Wang, Zhen Wu et al.

This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games. We reformulate the game as a regenerative problem with deterministic cycles, which allows policy evaluation (PE), policy improvement (PI), and population measure estimation to be carried out cycle by cycle. Within this formulation, we approximate the population measure by a particle system and update it using a one-step random mapping induced by the Euler-Maruyama discretization of the state dynamics. This update transports a mini-batch of particles from one cycle to the next, avoiding sequential trajectory simulation over the entire time horizon at each iteration. The PE and PI subproblems are formulated through the relation between consecutive cycles, with adversarial training used for evaluation and averaged optimization used for improvement. The resulting method is efficient and scalable in high dimensions, as it avoids the direct solution of the coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, the full simulation of trajectories to estimate the population measure, the explicit computation of conditional expectations in policy evaluation, and pointwise optimization in policy improvement. Numerical experiments demonstrate that the proposed method effectively handles dimensions up to 10,000.

Shupeng Wang, George Em Karniadakis

Physics-Informed Neural Networks (PINNs) have been widely used for solving partial differential equations (PDEs) of different types, including fractional PDEs (fPDES) [29]. Herein, we propose a new general (quasi) Monte Carlo PINN for solving fPDEs on irregular domains. Specifically, instead of approximating fractional derivatives by Monte Carlo approximations of integrals as was done previously in [31], we use a more general Monte Carlo approximation method to solve different fPDEs, which is valid for fractional differentiation under any definition. Moreover, based on the ensemble probability density function, the generated nodes are all located in denser regions near the target point where we perform the differentiation. This has an unexpected connection with known finite difference methods on non-equidistant or nested grids, and hence our method inherits their advantages. At the same time, the generated nodes exhibit a block-like dense distribution, leading to a good computational efficiency of this approach. We present the framework for using this algorithm and apply it to several examples. Our results demonstrate the effectiveness of GMC-PINNs in dealing with irregular domain problems and show a higher computational efficiency compared to the original fPINN method. We also include comparisons with the Monte Carlo fPINN [31]. Finally, we use examples to demonstrate the effectiveness of the method in dealing with fuzzy boundary location problems, and then use the method to solve the coupled 3D fractional Bloch-Torrey equation defined in the ventricular domain of the human brain, and compare the results with classical numerical methods.