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ODENet is a deep neural network architecture in which a stacking structure of ResNet is implemented with an ordinary differential equation (ODE) solver. It can reduce the number of parameters and strike a balance between accuracy and…
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by…
In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…
Exploding predictive AI has enabled fast yet effective evaluation and decision-making in modern chip physical design flows. State-of-the-art frameworks typically include the objective of minimizing the mean square error (MSE) between the…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…
Online learning with limited information feedback (bandit) tries to solve the problem where an online learner receives partial feedback information from the environment in the course of learning. Under this setting, Flaxman et al.[8]…
Orthogonality constrained optimization is widely used in applications from science and engineering. Due to the nonconvex orthogonality constraints, many numerical algorithms often can hardly achieve the global optimality. We aim at…
We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate…
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical…
This paper is concerned with the theory, construction and application of variable-stepsize implicit Peer two-step methods that are super-convergent for variable stepsizes, i.e., preserve their classical order achieved for uniform stepsizes…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
When equipped with efficient optimization algorithms, the over-parameterized neural networks have demonstrated high level of performance even though the loss function is non-convex and non-smooth. While many works have been focusing on…
We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…