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Computational graphs for matrix functions (2023)
Journal Article
Jarlebring, E., Fasi, M., & Ringh, E. (2023). Computational graphs for matrix functions. ACM Transactions on Mathematical Software, 48(4), 1-35. https://doi.org/10.1145/3568991

Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve them, and ev... Read More about Computational graphs for matrix functions.

CPFloat: A C library for simulating low-precision arithmetic (2023)
Journal Article
Fasi, M., & Mikaitis, M. (2023). CPFloat: A C library for simulating low-precision arithmetic. ACM Transactions on Mathematical Software, 49(2), 1-32. https://doi.org/10.1145/3585515

One can simulate low-precision floating-point arithmetic via software by executing each arithmetic operation in hardware and then rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standa... Read More about CPFloat: A C library for simulating low-precision arithmetic.

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores (2023)
Journal Article
Fasi, M., Higham, N. J., Lopez, F., Mary, T., & Mikaitis, M. (2023). Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores. SIAM Journal on Scientific Computing, 45(1), https://doi.org/10.1137/21M1465032

In multiword arithmetic, a matrix is represented as the unevaluated sum of two or more lower precision matrices, and a matrix product is formed by multiplying the constituents in low precision. We investigate the use of multiword arithmetic for impro... Read More about Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores.

Dynamic Unary Convolution in Transformers (2023)
Journal Article
Duan, H., Long, Y., Wang, S., Zhang, H., Willcocks, C. G., & Shao, L. (2023). Dynamic Unary Convolution in Transformers. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(11), 12747 - 12759. https://doi.org/10.1109/tpami.2022.3233482

It is uncertain whether the power of transformer architectures can complement existing convolutional neural networks. A few recent attempts have combined convolution with transformer design through a range of structures in series, where the main cont... Read More about Dynamic Unary Convolution in Transformers.

The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations (2022)
Journal Article
Dmytryshyn, A., Fasi, M., & Gulliksson, M. (2022). The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations. Applied Mathematics and Computation, 435, Article 127458. https://doi.org/10.1016/j.amc.2022.127458

Recent years have seen a renewal of interest in multi-term linear matrix equations, as these have come to play a role in a number of important applications. Here, we consider the solution of such equations by means of the dynamical functional particl... Read More about The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations.

A multiresolution Discrete Element Method for triangulated objects with implicit time stepping (2022)
Journal Article
Noble, P., & Weinzierl, T. (2022). A multiresolution Discrete Element Method for triangulated objects with implicit time stepping. SIAM Journal on Scientific Computing, 44(4), A2121-A2149. https://doi.org/10.1137/21m1421842

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are nonspherical. The most expensive part within such a simulation code is the colli... Read More about A multiresolution Discrete Element Method for triangulated objects with implicit time stepping.

Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code (2022)
Journal Article
Zhang, H., Weinzierl, T., Schulz, H., & Li, B. (2022). Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code. Monthly Notices of the Royal Astronomical Society, 515(2), 2464-2482. https://doi.org/10.1093/mnras/stac1991

The spherical collapse scenario has great importance in cosmology since it captures several crucial aspects of structure formation. The presence of self-similar solutions in the Einstein-de Sitter (EdS) model greatly simplifies its analysis, making i... Read More about Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code.

Dynamic task fusion for a block-structured finite volume solver over a dynamically adaptive mesh with local time stepping (2022)
Book Chapter
Li, B., Schulz, H., Weinzierl, T., & Zhang, H. (2022). Dynamic task fusion for a block-structured finite volume solver over a dynamically adaptive mesh with local time stepping. In High Performance Computing 37th International Conference, ISC High Performance 2022, Hamburg, Germany, May 29 – June 2, 2022, Proceedings (153-173). Springer Verlag. https://doi.org/10.1007/978-3-031-07312-0_8

Load balancing of generic wave equation solvers over dynamically adaptive meshes with local time stepping is dicult, as the load changes with every time step. Task-based programming promises to mitigate the load balancing problem. We study a Finite V... Read More about Dynamic task fusion for a block-structured finite volume solver over a dynamically adaptive mesh with local time stepping.

Stochastic rounding: implementation, error analysis and applications (2022)
Journal Article
Croci, M., Fasi, M., Higham, N. J., Mary, T., & Mikaitis, M. (2022). Stochastic rounding: implementation, error analysis and applications. Royal Society Open Science, 9(3), Article 211631. https://doi.org/10.1098/rsos.211631

Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in a finite precision number system. The probability of choosing either of these two numbers is 1 minus their relative distance to x. This rounding mode was first... Read More about Stochastic rounding: implementation, error analysis and applications.

Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models (2021)
Journal Article
Bond-Taylor, S., Leach, A., Long, Y., & Willcocks, C. G. (2021). Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11), 7327-7347. https://doi.org/10.1109/tpami.2021.3116668

Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including run-time, diversit... Read More about Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models.

Deep Learning Protein Conformational Space with Convolutions and Latent Interpolations (2021)
Journal Article
Ramaswamy, V. K., Musson, S. C., Willcocks, C. G., & Degiacomi, M. T. (2021). Deep Learning Protein Conformational Space with Convolutions and Latent Interpolations. Physical Review X, 11(1), Article 011052. https://doi.org/10.1103/physrevx.11.011052

Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein conformational... Read More about Deep Learning Protein Conformational Space with Convolutions and Latent Interpolations.