MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data

Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques. Motivated by this, we explore whether a similar approach can be applied to scientific foundation models (SFMs). Our methodology is structured as follows: (i) we collect low-cost physics-informed neural network (PINN)-based approximated prior data in the form of solutions to partial differential equations (PDEs) constructed through an arbitrary linear combination of mathematical dictionaries; (ii) we utilize Transformer architectures with self and cross-attention mechanisms to predict PDE solutions without knowledge of the governing equations in a zero-shot setting; (iii) we provide experimental evidence on the one-dimensional convection-diffusion-reaction equation, which demonstrate that pre-training remains robust even with approximated prior data, with only marginal impacts on test accuracy. Notably, this finding opens the path to pre-training SFMs with realistic, low-cost data instead of (or in conjunction with) numerical high-cost data. These results support the conjecture that SFMs can improve in a manner similar to LLMs, where fully cleaning the vast set of sentences crawled from the Internet is nearly impossible.

FastLRNR and Sparse Physics Informed Backpropagation

We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR). The approach exploits the low rank structure within LRNR and constructs a reduced neural network approximation that is much smaller in size. We call the smaller network FastLRNR. We show that backpropagation of FastLRNR can be substituted for that of LRNR, enabling a significant reduction in complexity. We apply SPInProp to a physics informed neural networks framework and demonstrate how the solution of parametrized partial differential equations is accelerated.

Bridging Dynamic Factor Models and Neural Controlled Differential Equations for Nowcasting GDP

Gross domestic product (GDP) nowcasting is crucial for policy-making as GDP growth is a key indicator of economic conditions. Dynamic factor models (DFMs) have been widely adopted by government agencies for GDP nowcasting due to their ability to handle irregular or missing macroeconomic indicators and their interpretability. However, DFMs face two main challenges: i) the lack of capturing economic uncertainties such as sudden recessions or booms, and ii) the limitation of capturing irregular dynamics from mixed-frequency data. To address these challenges, we introduce NCDENow, a novel GDP nowcasting framework that integrates neural controlled differential equations (NCDEs) with DFMs. This integration effectively handles the dynamics of irregular time series. NCDENow consists of 3 main modules: i) factor extraction leveraging DFM, ii) dynamic modeling using NCDE, and iii) GDP growth prediction through regression. We evaluate NCDENow against 6 baselines on 2 real-world GDP datasets from South Korea and the United Kingdom, demonstrating its enhanced predictive capability. Our empirical results favor our method, highlighting the significant potential of integrating NCDE into nowcasting models. Our code and dataset are available at https://github.com/sklim84/NCDENow_CIKM2024.

Parameterized Physics-informed Neural Networks for Parameterized PDEs

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known "failure modes".

MimiQ: Low-Bit Data-Free Quantization of Vision Transformers

Data-free quantization (DFQ) is a technique that creates a lightweight network from its full-precision counterpart without the original training data, often through a synthetic dataset. Although several DFQ methods have been proposed for vision transformer (ViT) architectures, they fail to achieve efficacy in low-bit settings. Examining the existing methods, we identify that their synthetic data produce misaligned attention maps, while those of the real samples are highly aligned. From the observation of aligned attention, we find that aligning attention maps of synthetic data helps to improve the overall performance of quantized ViTs. Motivated by this finding, we devise \aname, a novel DFQ method designed for ViTs that focuses on inter-head attention similarity. First, we generate synthetic data by aligning head-wise attention responses in relation to spatial query patches. Then, we apply head-wise structural attention distillation to align the attention maps of the quantized network to those of the full-precision teacher. The experimental results show that the proposed method significantly outperforms baselines, setting a new state-of-the-art performance for data-free ViT quantization.

Graph Signal Processing for Cross-Domain Recommendation

Cross-domain recommendation (CDR) extends conventional recommender systems by leveraging user-item interactions from dense domains to mitigate data sparsity and the cold start problem. While CDR offers substantial potential for enhancing recommendation performance, most existing CDR methods suffer from sensitivity to the ratio of overlapping users and intrinsic discrepancy between source and target domains. To overcome these limitations, in this work, we explore the application of graph signal processing (GSP) in CDR scenarios. We propose CGSP, a unified CDR framework based on GSP, which employs a cross-domain similarity graph constructed by flexibly combining target-only similarity and source-bridged similarity. By processing personalized graph signals computed for users from either the source or target domain, our framework effectively supports both inter-domain and intra-domain recommendations. Our empirical evaluation demonstrates that CGSP consistently outperforms various encoder-based CDR approaches in both intra-domain and inter-domain recommendation scenarios, especially when the ratio of overlapping users is low, highlighting its significant practical implication in real-world applications.

Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization

Time series forecasting has been an essential field in many different application areas, including economic analysis, meteorology, and so forth. The majority of time series forecasting models are trained using the mean squared error (MSE). However, this training based on MSE causes a limitation known as prediction delay. The prediction delay, which implies the ground-truth precedes the prediction, can cause serious problems in a variety of fields, e.g., finance and weather forecasting -- as a matter of fact, predictions succeeding ground-truth observations are not practically meaningful although their MSEs can be low. This paper proposes a new perspective on traditional time series forecasting tasks and introduces a new solution to mitigate the prediction delay. We introduce a continuous-time gated recurrent unit (GRU) based on the neural ordinary differential equation (NODE) which can supervise explicit time-derivatives. We generalize the GRU architecture in a continuous-time manner and minimize the prediction delay through our time-derivative regularization. Our method outperforms in metrics such as MSE, Dynamic Time Warping (DTW) and Time Distortion Index (TDI). In addition, we demonstrate the low prediction delay of our method in a variety of datasets.

DataFreeShield: Defending Adversarial Attacks without Training Data

Recent advances in adversarial robustness rely on an abundant set of training data, where using external or additional datasets has become a common setting. However, in real life, the training data is often kept private for security and privacy issues, while only the pretrained weight is available to the public. In such scenarios, existing methods that assume accessibility to the original data become inapplicable. Thus we investigate the pivotal problem of data-free adversarial robustness, where we try to achieve adversarial robustness without accessing any real data. Through a preliminary study, we highlight the severity of the problem by showing that robustness without the original dataset is difficult to achieve, even with similar domain datasets. To address this issue, we propose DataFreeShield, which tackles the problem from two perspectives: surrogate dataset generation and adversarial training using the generated data. Through extensive validation, we show that DataFreeShield outperforms baselines, demonstrating that the proposed method sets the first entirely data-free solution for the adversarial robustness problem.

PANDA: Expanded Width-Aware Message Passing Beyond Rewiring

Recent research in the field of graph neural network (GNN) has identified a critical issue known as "over-squashing," resulting from the bottleneck phenomenon in graph structures, which impedes the propagation of long-range information. Prior works have proposed a variety of graph rewiring concepts that aim at optimizing the spatial or spectral properties of graphs to promote the signal propagation. However, such approaches inevitably deteriorate the original graph topology, which may lead to a distortion of information flow. To address this, we introduce an expanded width-aware (PANDA) message passing, a new message passing paradigm where nodes with high centrality, a potential source of over-squashing, are selectively expanded in width to encapsulate the growing influx of signals from distant nodes. Experimental results show that our method outperforms existing rewiring methods, suggesting that selectively expanding the hidden state of nodes can be a compelling alternative to graph rewiring for addressing the over-squashing.

Efficiently Parameterized Neural Metriplectic Systems

Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic data. Besides being provably energy conserving and entropy stable, the proposed approach comes with approximation results demonstrating its ability to accurately learn metriplectic dynamics from data as well as an error estimate indicating its potential for generalization to unseen timescales when approximation error is low. Examples are provided which illustrate performance in the presence of both full state information as well as when entropic variables are unknown, confirming that the proposed approach exhibits superior accuracy and scalability without compromising on model expressivity.