More Like this

1. Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

   https://doi.org/10.3390/a13110278  

   Tymochko, Sarah; Munch, Elizabeth; Khasawneh, Firas A. (November 2020, Algorithms)

   null (Ed.)

   Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. In an experimental setting, this transition could lead to incorrect data or damage to the entire experiment. While standard persistent homology has been used in this setting, it usually requires analyzing a collection of persistence diagrams, which in turn drives up the computational cost considerably. Using zigzag persistence, we can capture topological changes in the state space of the dynamical system in only one persistence diagram. Here, we present Bifurcations using ZigZag (BuZZ), a one-step method to study and detect bifurcations using zigzag persistence. The BuZZ method is successfully able to detect this type of behavior in two synthetic examples as well as an example dynamical system. 

   more » « less
2. Query-driven Segment Selection for Ranking Long Documents

   https://doi.org/10.1145/3459637.3482101  

   Kim, Youngwoo; Rahimi, Razieh; Bonab, Hamed; Allan, James (October 2021, Proceedings of The 30th ACM International Conference on Information and Knowledge Management (CIKM '21))

   Transformer-based rankers have shown the state-of-the-art performance, but their self-attention operation is mostly unable to process long sequences. One of the common approaches to train these rankers is to heuristically select some segments of each document, such as the first segment, as training data. However, these segments may not contain the query-related parts of documents. To address this problem, we propose the query-driven segment selection from long documents to build training data for transformer-based rankers. The segment selector provides relevant samples with more accurate labels and non-relevant samples which are harder to be predicted. The experimental results show that the basic BERT-based ranker trained with the proposed segment selector significantly outperforms that trained by the heuristically selected segments, and performs equally to the state-of-the-art model with localized self-attention that can process longer input sequences. We also demonstrate that training with our segment selector, there is not much gain from feeding input sequences larger than 200 words. Our findings open up new opportunities to design efficient transformer-based rankers. 

   more » « less
3. Discovering sparse interpretable dynamics from partial observations

   https://doi.org/10.1038/s42005-022-00987-z  

   Lu, Peter Y.; Ariño Bernad, Joan; Soljačić, Marin (August 2022, Communications Physics)

   Abstract Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential equation (ODE) and partial differential equation (PDE) systems. 

   more » « less
4. FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model for Dynamical Simulation

   https://doi.org/10.1002/adts.202500062  

   Song, Zezheng; Yuan, Jiaxin; Yang, Haizhao (April 2025, Advanced Theory and Simulations)

   Abstract The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing interest in using neural networks to solve differential equations in a data‐driven manner. However, existing methods are either limited to specific types of differential equations or require large amounts of data for training. This restricts their practicality in many real‐world applications, where data is often scarce or expensive to obtain. To address this, a novel multi‐modal foundation model, namedFMint(FoundationModel based onInitialization) is proposed, to bridge the gap between human‐designed and data‐driven models for the fast simulation of dynamical systems. Built on a decoder‐only transformer architecture with in‐context learning, FMint utilizes both numerical and textual data to learn a universal error correction scheme for dynamical systems, using prompted sequences of coarse solutions from traditional solvers. The model is pre‐trained on a corpus of 400K ordinary differential equations (ODEs), and extensive experiments are performed on challenging ODEs that exhibit chaotic behavior and of high dimensionality. The results demonstrate the effectiveness of the proposed model in terms of both accuracy and efficiency compared to classical numerical solvers, highlighting FMint's potential as a general‐purpose solver for dynamical systems. This approach achieves an accuracy improvement of 1 to 2 orders of magnitude over state‐of‐the‐art dynamical system simulators, and delivers a 5X speedup compared to traditional numerical algorithms. The code for FMint is available athttps://github.com/margotyjx/FMint. 

   more » « less
5. Generating Euler Diagrams Through Combinatorial Optimization

   https://doi.org/10.1111/cgf.15089  

   Rottmann, Peter; Rodgers, Peter; Yan, Xinyuan; Archambault, Daniel; Wang, Bei; Haunert, Jan‐Henrik (June 2024, Computer Graphics Forum)

   Can a given set system be drawn as an Euler diagram? We present the first method that correctly decides this question for arbitrary set systems if the Euler diagram is required to represent each set with a single connected region. If the answer is yes, our method constructs an Euler diagram. If the answer is no, our method yields an Euler diagram for a simplified version of the set system, where a minimum number of set elements have been removed. Further, we integrate known wellformedness criteria for Euler diagrams as additional optimization objectives into our method. Our focus lies on the computation of a planar graph that is embedded in the plane to serve as the dual graph of the Euler diagram. Since even a basic version of this problem is known to be NP‐hard, we choose an approach based on integer linear programming (ILP), which allows us to compute optimal solutions with existing mathematical solvers. For this, we draw upon previous research on computing planar supports of hypergraphs and adapt existing ILP building blocks for contiguity‐constrained spatial unit allocation and the maximum planar subgraph problem. To generate Euler diagrams for large set systems, for which the proposed simplification through element removal becomes indispensable, we also present an efficient heuristic. We report on experiments with data from MovieDB and Twitter. Over all examples, including 850 non‐trivial instances, our exact optimization method failed only for one set system to find a solution without removing a set element. However, with the removal of only a few set elements, the Euler diagrams can be substantially improved with respect to our wellformedness criteria. 

   more » « less