Wei Liu

Zhilu Lai, Wei Liu, Xudong Jian et al.

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or mechanical structures), which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this paper proposes a framework -- termed Neural Modal ODEs -- to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. Neural Ordinary Differential Equations -- Neural ODEs are exploited as the deep learning operator. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed Neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the abstract mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via physics-informed Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigen-analysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to outperform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, i.e., the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.

Marcus Haywood-Alexander, Wei Liu, Kiran Bacsa et al.

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this paper, the spectrum of physics-enhanced machine learning methods, expressed across the defining axes of physics and data, is discussed by engaging in a comprehensive exploration of its characteristics, usage, and motivations. In doing so, we present a survey of recent applications and developments of PEML techniques, revealing the potency of PEML in addressing complex challenges. We further demonstrate application of select such schemes on the simple working example of a single degree-of-freedom Duffing oscillator, which allows to highlight the individual characteristics and motivations of different `genres' of PEML approaches. To promote collaboration and transparency, and to provide practical examples for the reader, the code generating these working examples is provided alongside this paper. As a foundational contribution, this paper underscores the significance of PEML in pushing the boundaries of scientific and engineering research, underpinned by the synergy of physical insights and machine learning capabilities.

Xiaodi Li, Yang Xiao, Munhwan Lee et al.

Patient-trial matching requires reasoning over long, heterogeneous electronic health records (EHRs) and complex eligibility criteria, posing significant challenges for scalability, generalization, and computational efficiency. Existing approaches either rely on full-document processing with large language models (LLMs), which is computationally expensive, or use traditional machine learning methods that struggle to capture unstructured clinical narratives. In this work, we propose a lightweight framework that combines retrieval-augmented generation and large language model-based modeling for scalable patient-trial matching. The framework explicitly separates two key components: retrieval-augmented generation is used to identify clinically relevant segments from long EHRs, reducing input complexity, while large language models are used to encode these selected segments into informative representations. These representations are further refined through dimensionality reduction and modeled using lightweight predictors, enabling efficient and scalable downstream classification. We evaluate the proposed approach on multiple public benchmarks (n2c2, SIGIR, TREC 2021/2022) and a real-world multimodal dataset from Mayo Clinic (MCPMD). Results show that retrieval-based information selection significantly reduces computational burden while preserving clinically meaningful signals. We further demonstrate that frozen LLMs provide strong representations for structured clinical data, whereas fine-tuning is essential for modeling unstructured clinical narratives. Importantly, the proposed lightweight pipeline achieves performance comparable to end-to-end LLM approaches with substantially lower computational cost.

Yuelin Hu, Zhenbo Yu, Zhengxue Cheng et al.

Many continual-learning methods modify gradients upstream (e.g., projection, penalty rescaling, replay mixing) while treating Adam as a neutral backend. We show this composition has a hidden failure mode. In a high-overlap, non-adaptive 8-domain continual LM, all shared-routing projection baselines collapse close to vanilla forgetting (12.5--12.8 vs. 13.2). A 0.5% replay buffer is the strongest shared alternative but still reaches 11.6, while fixed-strength decoupling falls below vanilla at 14.1. Only adaptive decoupled routing remains stable at 9.4, improving over vanilla by 3.8 units. On a 16-domain stream, its gain over the strongest shared-routing projection baseline grows to 4.5--4.8 units. The failure is largely invisible on clean benchmarks. We explain this effect through Adam's second-moment pathway: in the tested regime, projection induces a 1/(1-alpha) inflation of the old-direction effective learning rate, matching measurements within 8% across eight alpha values. The same conflict appears with penalty methods, replay mixing, and at 7B scale under LoRA. Our fix routes the modified gradient only to the first moment while preserving magnitude-faithful second-moment statistics, with overlap-aware adaptive strength. This simple change is the only tested configuration that consistently avoids collapse across methods, optimizers, and scale.

Wei Liu, Zhilu Lai, Kiran Bacsa et al.

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.