mechanistic model critique

Existing dynamical system forecasting models suffer from significant limitations in long-horizon prediction accuracy, modeling of long-range dependencies, capture of chaotic evolution, and extrapolation under scarce-data conditions. This paper introduces the first Mamba-enhanced state-space model (SSM) for physics-informed machine learning (PIML), innovatively embedding Mamba’s structured state evolution mechanism into a neural operator framework while integrating parameter remapping and quantitative systems pharmacology priors. We design a rigorous extrapolation benchmark encompassing chaotic systems and multiscale dynamics to systematically address generalization bottlenecks under long-range dependencies, strong nonlinearity, and data scarcity. Experiments demonstrate state-of-the-art performance across diverse interpolation and extrapolation tasks with the lowest computational overhead. In real-world evaluation of anticancer drug efficacy, the method achieves highly robust predictions using only minimal clinical data—marking a critical advance in interpretable, sample-efficient PIML for complex biological dynamics.

Integrating physics-based and machine learning models for dynamic system modeling remains challenging due to difficulties in unifying multi-model representations, handling algebraic loops, and managing discontinuous events within a coherent framework. Method: This paper proposes a learnable and interpretable hybrid modeling paradigm built upon a novel wildcard architecture—the first to enable unified symbolic representation of algebraic, discrete, and differential equations—supporting end-to-end differentiable joint optimization of physics-informed and data-driven components. Grounded in systems theory and symbolic modeling principles, the approach inherently avoids algebraic loops and explicitly models discontinuities. Contribution/Results: Experiments demonstrate that the framework automatically identifies and resolves diverse dual-model compositions, achieving significant improvements over state-of-the-art methods in prediction accuracy, model interpretability, and cross-scenario generalizability.

This paper addresses discrete-time interconnected systems whose subsystem dynamics and interconnection topology are partially unknown. Method: We propose a data-driven, compositional approach to construct finite-state abstractions for formal verification and distributed controller synthesis. Subsystems are modeled individually from input-output data, and—novelly—the unknown static interconnection mapping is treated as a learnable object, enabling its symbolic abstraction. Compositionality and rigorous error propagation analysis ensure that the resulting abstraction strictly satisfies an approximate simulation relation. Contribution/Results: We theoretically establish scalability and verifiability of the abstraction. Experiments demonstrate substantial mitigation of the curse of dimensionality, enabling high-precision, low-complexity controller synthesis while preserving formal guarantees.

This work addresses the limited interpretability of existing state space models regarding their long-range dependency mechanisms, particularly the unclear relationship between modeling capacity and architectural design in real-world tasks. Focusing on the S4D model, we present the first systematic analysis of its kernel behavior in the context of source code vulnerability detection. By integrating time-domain and frequency-domain analyses, we demonstrate that S4D can function as a low-pass, band-pass, or high-pass filter depending on its architectural configuration. This finding reveals that the model’s ability to capture long-range dependencies is profoundly influenced by its architecture, thereby offering both theoretical insights and concrete guidance for designing more effective state space models.

This work addresses the limitations of current large language models (LLMs) in generating mechanistic models under partially observable conditions and diverse task objectives, where outputs often suffer from unreliability, coding errors, and lack of validity. To overcome these challenges, we propose the Neural Integrated Mechanistic Modeling (NIMM) evaluation framework and develop the NIMMGen agent system, which leverages an iterative refinement mechanism between neural networks and mechanistic models to substantially enhance code correctness, empirical validity, and interpretability. Our approach provides the first systematic assessment of LLM-generated mechanistic models under realistic conditions, enabling reliable digital twin construction and counterfactual intervention simulation. Experiments across three scientific datasets demonstrate that models generated by NIMMGen exhibit strong counterfactual reasoning capabilities in complex scenarios.

This work addresses the challenge of efficiently capturing structured dynamical behaviors, which traditional approaches to dynamical system learning often fail to achieve due to their reliance on high-complexity nonlinear function approximators. The authors propose a structure-first modeling paradigm that integrates wave-inspired causal interaction mechanisms with explicit state evolution units, yielding a fully explicit, hierarchical dynamical architecture free of algebraic loops. Notably, the model dispenses with implicit solvers and generates effective internal representations by training only the readout layer. Experimental results demonstrate that as model depth increases, both representation quality and generalization performance improve significantly on nonlinear system identification tasks, thereby validating the efficacy of prioritizing interaction structure in model design.

This study addresses the challenge of unified modeling of source/sink dynamics, cyclic behavior, and topology-constrained transport in complex dynamical systems. By integrating the continuous theory of Helmholtz–Hodge decomposition with discrete data-driven approaches, the authors propose a structured flow modeling paradigm based on graph vector fields (GVFs) and gradient–curl–harmonic decompositions over simplicial complexes. They develop a multi-level modeling strategy that spans from high expressivity to low computational cost through parameterized conditional models and a simplified Hodge representation. A cross-domain validation and diagnosis–simplification iterative pipeline is further designed to ensure model interpretability while achieving computational efficiency. The framework systematically elucidates the trade-offs among model complexity, interpretability, and predictive performance.

This work proposes a brain-inspired neural computing framework designed to unify learning, memory, control, and optimization within a single architecture that is scalable, robust, and energy-efficient. By integrating principles from energy landscapes, gradient flows, control theory, and neuroscience, the study introduces a novel paradigm that transcends conventional feedforward networks and backpropagation. Key mechanisms include continuous-time Hopfield networks, dense associative memory, oscillator-based dynamics, and proximal descent dynamics. The resulting architecture achieves markedly improved computational efficiency and biological plausibility, demonstrating superior performance in data-driven control, constrained reconstruction, and large-scale optimization tasks.

This study addresses the limitations of traditional state-space models, which rely on predefined nonlinear dynamics and struggle with theoretically under-specified complex systems, as well as the high computational cost of Bayesian inference in Gaussian process state-space models for moderately long sequences. To overcome these challenges, the authors propose two enhanced Gibbs sampling strategies that substantially improve sampling efficiency and convergence reliability. By integrating confirmatory factor analysis to construct an identifiable and interpretable measurement structure, they develop a comprehensive framework for learning nonlinear latent dynamical systems. Simulation studies validate the accuracy of posterior inference, while two empirical applications demonstrate the method’s practical utility and interpretability. An open-source implementation is provided, offering researchers an efficient and feasible workflow for empirical analysis.

This work addresses the structural bias introduced by arbitrary variable ordering in multivariate time series modeling, which violates the inherent exchangeability of variables in real-world systems. To resolve this, the authors propose VI 2D SSM, a two-dimensional state space model that respects permutation equivariance by decomposing dynamics into local self-evolution and global aggregated interactions, thereby eliminating dependence on variable order. They provide the first theoretical characterization of the canonical form for permutation-equivariant linear coupling, proving that ordered recursive architectures are structurally suboptimal and reducing inter-variable dependency depth from O(C) to O(1). By further integrating multi-scale temporal dynamics and spectral representations, they develop a unified architecture, VI 2D Mamba, which achieves state-of-the-art performance across forecasting, classification, and anomaly detection tasks, demonstrating the advantages of symmetry-preserving modeling in both structural scalability and empirical effectiveness.