Robust Diffusion Models for Adversarial Purification

Diffusion models (DMs) based adversarial purification (AP) has shown to be the most powerful alternative to adversarial training (AT). However, these methods neglect the fact that pre-trained diffusion models themselves are not robust to adversarial attacks as well. Additionally, the diffusion process can easily destroy semantic information and generate a high quality image but totally different from the original input image after the reverse process, leading to degraded standard accuracy. To overcome these issues, a natural idea is to harness adversarial training strategy to retrain or fine-tune the pre-trained diffusion model, which is computationally prohibitive. We propose a novel robust reverse process with adversarial guidance, which is independent of given pre-trained DMs and avoids retraining or fine-tuning the DMs. This robust guidance can not only ensure to generate purified examples retaining more semantic content but also mitigate the accuracy-robustness trade-off of DMs for the first time, which also provides DM-based AP an efficient adaptive ability to new attacks. Extensive experiments are conducted to demonstrate that our method achieves the state-of-the-art results and exhibits generalization against different attacks.

Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous confidence intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning.

Adversarial Training on Purification (AToP): Advancing Both Robustness and Generalization

The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot generalize well to unseen attacks. Another effective defense technique based on adversarial purification (AP) can enhance generalization but cannot achieve optimal robustness. Meanwhile, both methods share one common limitation on the degraded standard accuracy. To mitigate these issues, we propose a novel framework called Adversarial Training on Purification (AToP), which comprises two components: perturbation destruction by random transforms (RT) and purifier model fine-tuned (FT) by adversarial loss. RT is essential to avoid overlearning to known attacks resulting in the robustness generalization to unseen attacks and FT is essential for the improvement of robustness. To evaluate our method in an efficient and scalable way, we conduct extensive experiments on CIFAR-10, CIFAR-100, and ImageNette to demonstrate that our method achieves state-of-the-art results and exhibits generalization ability against unseen attacks.

Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo

Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when demanding high accuracy. To address this, we propose an approximate Thompson sampling strategy, utilizing underdamped Langevin Monte Carlo, where the latter is the go-to workhorse for simulations of high-dimensional posteriors. Based on the standard smoothness and log-concavity conditions, we study the accelerated posterior concentration and sampling using a specific potential function. This design improves the sample complexity for realizing logarithmic regrets from $\mathcal{\tilde O}(d)$ to $\mathcal{\tilde O}(\sqrt{d})$. The scalability and robustness of our algorithm are also empirically validated through synthetic experiments in high-dimensional bandit problems.

Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface with Deep Generative Model

Biased enhanced sampling methods utilizing collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to high intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While methods like temperature-accelerated molecular dynamics (TAMD) can adopt many CVs in a simulation, unbiasing the simulation requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We test the score-based diffusion unbiasing method on TAMD simulations. The results demonstrate that this unbiasing approach significantly outperforms traditional unbiasing methods, and can generate accurate unbiased conformational ensembles for simulations with a number of CVs higher than usual ranges.

B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions

Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended DeepONet to allow multiple input functions in different Banach spaces. MIONet offers flexibility in training dataset grid spacing, without constraints on output location. However, it requires offline inputs and cannot handle varying sequence lengths in testing datasets, limiting its real-time application in dynamic complex systems. This work redesigns MIONet, integrating Long Short Term Memory (LSTM) to learn neural operators from time-dependent data. This approach overcomes data discretization constraints and harnesses LSTM's capability with variable-length, real-time data. Factors affecting learning performance, like algorithm extrapolation ability are presented. The framework is enhanced with uncertainty quantification through a novel Bayesian method, sampling from MIONet parameter distributions. Consequently, we develop the B-LSTM-MIONet, incorporating LSTM's temporal strengths with Bayesian robustness, resulting in a more precise and reliable model for noisy datasets.

Fair Supervised Learning with A Simple Random Sampler of Sensitive Attributes

As the data-driven decision process becomes dominating for industrial applications, fairness-aware machine learning arouses great attention in various areas. This work proposes fairness penalties learned by neural networks with a simple random sampler of sensitive attributes for non-discriminatory supervised learning. In contrast to many existing works that critically rely on the discreteness of sensitive attributes and response variables, the proposed penalty is able to handle versatile formats of the sensitive attributes, so it is more extensively applicable in practice than many existing algorithms. This penalty enables us to build a computationally efficient group-level in-processing fairness-aware training framework. Empirical evidence shows that our framework enjoys better utility and fairness measures on popular benchmark data sets than competing methods. We also theoretically characterize estimation errors and loss of utility of the proposed neural-penalized risk minimization problem.

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured Deep Operator Network (DeepONet) framework that effectively combines low and high-fidelity datasets, leveraging the strengths of each. In our methodology, we began by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network's output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the Trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts.

D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. In our study, we propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. We demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present four numerical examples to validate its performance.

Backdiff: a diffusion model for generalized transferable protein backmapping

Coarse-grained (CG) models play a crucial role in the study of protein structures, protein thermodynamic properties, and protein conformation dynamics. Due to the information loss in the coarse-graining process, backmapping from CG to all-atom configurations is essential in many protein design and drug discovery applications when detailed atomic representations are needed for in-depth studies. Despite recent progress in data-driven backmapping approaches, devising a backmapping method that can be universally applied across various CG models and proteins remains unresolved. In this work, we propose BackDiff, a new generative model designed to achieve generalization and reliability in the protein backmapping problem. BackDiff leverages the conditional score-based diffusion model with geometric representations. Since different CG models can contain different coarse-grained sites which include selected atoms (CG atoms) and simple CG auxiliary functions of atomistic coordinates (CG auxiliary variables), we design a self-supervised training framework to adapt to different CG atoms, and constrain the diffusion sampling paths with arbitrary CG auxiliary variables as conditions. Our method facilitates end-to-end training and allows efficient sampling across different proteins and diverse CG models without the need for retraining. Comprehensive experiments over multiple popular CG models demonstrate BackDiff's superior performance to existing state-of-the-art approaches, and generalization and flexibility that these approaches cannot achieve. A pretrained BackDiff model can offer a convenient yet reliable plug-and-play solution for protein researchers, enabling them to investigate further from their own CG models.