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1. An Explicit Hermite-Taylor Method for the Schrödinger Equation

   https://doi.org/10.4208/cicp.080815.211116a  

   Appelö, Daniel; Kreiss, Gunilla; Wang, Siyang (May 2017, Communications in Computational Physics)

   Abstract An explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method. 

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2. An Extension of Explicit Coupling for Fluid–Structure Interaction Problems

   https://doi.org/10.3390/math9151747  

   Bukač, Martina (August 2021, Mathematics)

   null (Ed.)

   We present an extension of a non-iterative, partitioned method previously designed and used to model the interaction between an incompressible, viscous fluid and a thick elastic structure. The original method is based on the Robin boundary conditions and it features easy implementation and unconditional stability. However, it is sub-optimally accurate in time, yielding only O(Δt12) rate of convergence. In this work, we propose an extension of the method designed to improve the sub-optimal accuracy. We analyze the stability properties of the proposed method, showing that the method is stable under certain conditions. The accuracy and stability of the method are computationally investigated, showing a significant improvement in the accuracy when compared to the original scheme, and excellent stability properties. Furthermore, since the method depends on a combination parameter used in the Robin boundary conditions, whose values are problem specific, we suggest and investigate formulas according to which this parameter can be determined. 

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3. Automated Generation of Stand-Alone Source Codes for Software Libraries

   Machi, Lucas; Carscadden, Henry L; Kuhlman, Chris J; Machi, Dustin; Ravi, S S. (October 2021, Software Engineering and Data Engineering)

   Networks are pervasive in society: infrastructures (e.g., telephone), commercial sectors (e.g., banking), and biological and genomic systems can be represented as networks. Consequently, there are software libraries that analyze networks. Containers (e.g., Docker, Singularity), which hold both runnable codes and their execution environments, are increasingly utilized by analysts to run codes in a platform-independent fashion. Portability is further enhanced by not only providing software library methods, but also the driver code (i.e., main() method) for each library method. In this way, a user only has to know the invocation for the main() method that is in the container. In this work, we describe an automated approach for generating a main() method for each software library method. A single intermediate representation (IR) format is used for all library methods, and one IR instance is populated for one library method by parsing its comments and method signature. An IR for the main() method is generated from that for the library method. A source code generator uses the main() method IR and a set of small, hand-generated source code templates|with variables in the templates that are automatically customized for a particular library method|to produce the source code main() method. We apply our approach to two widely used software libraries, SNAP and NetworkX, as exemplars, which combined have over 400 library methods. 

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4. Automated Generation of Stand-Alone Source Codes for Software Libraries

   Machi, L.; Carscadden, H.L.; Kuhlman, C.J.; Machi, D.; Ravi, S.S. (January 2021, ISCA 30th International Conference)

   Harris, F.; Wu, R.; Redei, A. (Ed.)

   Networks are pervasive in society: infrastructures (e.g., telephone), commercial sectors (e.g., banking), and biological and genomic systems can be represented as networks. Con- sequently, there are software libraries that analyze networks. Containers (e.g., Docker, Singularity), which hold both runnable codes and their execution environments, are in- creasingly utilized by analysts to run codes in a platform-independent fashion. Portability is further enhanced by not only providing software library methods, but also the driver code (i.e., main() method) for each library method. In this way, a user only has to know the invocation for the main() method that is in the container. In this work, we describe an automated approach for generating a main() method for each software library method. A single intermediate representation (IR) format is used for all library methods, and one IR instance is populated for one library method by parsing its comments and method signature. An IR for the main() method is generated from that for the library method. A source code generator uses the main() method IR and a set of small, hand-generated source code templates|with variables in the templates that are automatically customized for a particular library method|to produce the source code main() method. We apply our approach to two widely used software libraries, SNAP and NetworkX, as examplars, which combined have over 400 library methods. 

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5. Verification of Recurrent Neural Networks with Star Reachability

   https://doi.org/10.1145/3575870.3587128  

   Tran, Hoang Dung; Choi, Sung Woo; Yang, Xiaodong; Yamaguchi, Tomoya; Hoxha, Bardh; Prokhorov, Danil (May 2023, The 26th ACM International Conference on Hybrid Systems: Computation and Control)

   The paper extends the recent star reachability method to verify the robustness of recurrent neural networks (RNNs) for use in safety-critical applications. RNNs are a popular machine learning method for various applications, but they are vulnerable to adversarial attacks, where slightly perturbing the input sequence can lead to an unexpected result. Recent notable techniques for verifying RNNs include unrolling, and invariant inference approaches. The first method has scaling issues since unrolling an RNN creates a large feedforward neural network. The second method, using invariant sets, has better scalability but can produce unknown results due to the accumulation of overapproximation errors over time. This paper introduces a complementary verification method for RNNs that is both sound and complete. A relaxation parameter can be used to convert the method into a fast overapproximation method that still provides soundness guarantees. The method is designed to be used with NNV, a tool for verifying deep neural networks and learning-enabled cyber-physical systems. Compared to state-of-the-art methods, the extended exact reachability method is 10 × faster, and the overapproximation method is 100 × to 5000 × faster. 

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