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Video
We introduce a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only Hessian-vector products in two directions. Moreover; the computational overhead remains comparable to the first-order such as the gradient descent method. We show that the method has a local super-linear convergence and a global convergence rate of 0(∈-3/2) to satisfy the first-order and second-order conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first first-order-type algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2-Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over state-of-the-art first-order methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Nonconvex programming Mathematical optimization
- Resource Type:
- Video
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Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primal-dual interior-point methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximal-point or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve low-rank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. Kim-Chuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Semidefinite programming
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Sampling (Statistics) Differential equations Partial -- Numerical solutions Mathematical models Adaptive computing systems
- Resource Type:
- Video
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Video
Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Convex sets Mathematical optimization Computer science -- Mathematics
- Resource Type:
- Video
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Video
More than one hundred years ago, Albert Einstein published his Theory of General Relativity (GR). One year later, Karl Schwarzschild solved the GR equations for a non-rotating, spherical mass distribution; if this mass is sufficiently compact, even light cannot escape from within the so-called event horizon, and there is a mass singularity at the center. The theoretical concept of a 'black hole' was born, and was refined in the next decades by work of Penrose, Wheeler, Kerr, Hawking and many others. First indirect evidence for the existence of such black holes in our Universe came from observations of compact X-ray binaries and distant luminous quasars. I will discuss the forty-year journey, which my colleagues and I have been undertaking to study the mass distribution in the Center of our Milky Way from ever more precise, long-term studies of the motions of gas and stars as test particles of the space time. These studies show the existence of a four million solar mass object, which must be a single massive black hole, beyond any reasonable doubt.
Even date: 9/2/2023
Speaker: Prof. Reinhard GENZEL
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Physics and Cosmology and Astronomy
- Keywords:
- Nobel Prize winners Astrophysics Astronomy Deep space -- Milky Way Black holes (Astronomy) General relativity (Physics)
- Resource Type:
- Video
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Video
Universities conduct research for three reasons: to educate students, to contribute to society, and to understand the world. While society often holds a view of the scholar as a solitary and singular genius, in reality scholars today participate in a highly collaborative, worldwide search for shared understandings that stand the test of time and the scrutiny of others. The problems in the 21st century often demand effort by teams of researchers with resources at scale: laboratories and equipment, compute resources, and expert staffing. Working with faculty, students, and other stakeholders to identify the greatest opportunities and the resources needed to address them is both a privilege and a challenge for modern academic administrators. In this talk, I will share three examples: fostering collaborative proposal-writing; planning for shared capabilities in experimental facilities, data, and computation; and transforming academic structures.
Even date: 12/4/2023
Speaker: Prof. Kathryn Ann Moler
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Statistics and Research Methods
- Keywords:
- Research Science
- Resource Type:
- Video
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Video
In the context of hyperbolic systems of balance laws with dissipative source manifesting relaxation, recent pr"Ogress will be reported in the program of passing to the limit, in 1he BV setting, as the relaxation lime tends to zero.
Event date: 16/2/2023
Speaker: Prof. Constantine Dafermos (Brown University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Equilibrium -- Mathematical models Relaxation Differential equations Hyperbolic
- Resource Type:
- Video
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Video
Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
Event date: 19/1/2023
Speaker: Prof. Benoît Perthame (Sorbonne University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Biology and Mathematics and Statistics
- Keywords:
- Biomathematics Equations
- Resource Type:
- Video
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Video
We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by regions in which u > O and u < 0. The classical point of view of regarding the Prandtl equations as an evolution equation in x completely breaks down since u changes sign. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. This is a joint work with Sameer Iyer.
Event date: 14/3/2023
Speaker: Prof. Nader Masmoudi (New York University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Fluid dynamics -- Mathematical models
- Resource Type:
- Video
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Video
In this lecture I consider the fundamental, challenging and largely unsolved problem of deriving rigorously the most popular kinetic equations, starting from the laws governing the dynamics of microscopic systems. I plan to present classical and recent results, discussing also some present perspectives.
Event date: 30/3/2023
Speaker: Prof. Mario Pulvirenti (University of Roma La Sapienza)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models Kinetic theory of gases -- Mathematical models
- Resource Type:
- Video
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e-book
Astronomy is designed to meet the scope and sequence requirements of one- or two-semester introductory astronomy courses. The book begins with relevant scientific fundamentals and progresses through an exploration of the solar system, stars, galaxies and cosmology. The Astronomy textbook builds student understanding through the use of relevant analogies, clear and non-technical explanations, and rich illustrations. Mathematics is included in a flexible manner to meet the needs of individual instructors.
- Subjects:
- Cosmology and Astronomy
- Keywords:
- Textbooks Astronomy
- Resource Type:
- e-book
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Video
香港理工大學高等研究院於2023年4月21日成功舉辦以「綠色化工與分子篩催化」為題的公開講座（混合模式）。講座由中國工程院院士、中國石化上海石油化工研究院院長楊為民教授主講，吸引了來自亞洲、歐洲、北美10多個國家和地區的120多名現場及網上參加者。講座亦在嗶哩嗶哩、微博等多個社交媒體平台進行直播，在線觀看人數超過11,000人次。
講座由理大協理副校長（研究與創新）王鑽開教授以歡迎辭及講者介紹揭開序幕。楊教授介紹了其團隊在綠色化工領域的研究進展，包括基於分子篩催化材料的綠色化工技術開發與實踐，以及新型分子篩催化材料的應用，並分享了他對行業未來趨勢的展望。 隨後的問答環節由應用物理系客座教授曾適之教授主持，一眾參加者與楊教授進行了富有成果的交流。
- Subjects:
- Chemistry
- Keywords:
- Zeolites Catalysis Zeolite catalysts Green chemistry
- Resource Type:
- Video
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Video
Water shortage is one of the biggest challenges that humanity faces. Novel technologies to tackle the challenge of water scarcity are urgently needed. However, all the existing studies are based on bare fibers with diameter in the order of mm. This talk introduces a novel fog collection technology using microfibers fabricated by near-field electrospinning. The collection efficiency reaches a record high level. Systematic investigation reveals that the waterdrops are “visible” to fog droplets in the incoming air flow because of the relatively small size of the microfibers. Thus, the large waterdrops deflect the fog-carrying airflow to the satellite small waterdrops, which effectively intercept the fog droplets.
Event Date: 12/10/2023
Speaker: Prof. TAN Zhongchao (Founding Chair Professor, Vice Provost and Dean of Academic Affairs of the Eastern Institute of Technology in Ningbo, China)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Environmental Sciences and Mechanical Engineering
- Keywords:
- Fog Hydrology Water harvesting Water-supply
- Resource Type:
- Video
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Video
In the presentation, Prof. Chan shared Singapore’s long-term energy plan and research focus, as well as a few major initiatives on hydrogen application. He then introduced turquoise hydrogen and the catalytic decomposition of methane for hydrogen production, followed by an overview of the research activities on hydrogen and fuel cells at NTU over the last 30 years.
Event Date: 13/6/2023
Speaker: Prof. CHAN Siew Hwa (Nanyang Technological University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Electrical Engineering
- Keywords:
- Clean energy Hydrogen as fuel
- Resource Type:
- Video
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Video
The lecture commenced with a warm welcome address by Prof. CHEN Qingyan, Director of PAIR, followed by a brief speaker introduction by Prof. WANG Zuankai, Associate Vice President (Research and Innovation) of PolyU. In his presentation, Prof. Yang highlighted that urgent need for tissue/organ biomanufacturing owing to the shortage of donation for organ transplantation. He pointed out some challenges in the in vitro manufacturing of tissues/organs, particularly in relation to accurate design, precise fabrication, and functional induction, which underscore the imperative need for new methods for tissue/organ manufacturing. Next, Prof. Yang outlined the development roadmap of biomanufacturing and shared specific examples demonstrating the research progress in 3D bioprinting. In concluding his presentation, Prof. Yang shared his insights on the future direction for biomanufacturing, as well as some significant accomplishments by him and his team at Zhejiang University in the field.
A question-and-answer session moderated by Prof. Wang was followed. Both the online and on-site audience had a fruitful discussion with Prof. Yang.
Even date: 2/1/2024
Speaker: Prof. Huayong Yang (Zhejiang University)
Moderator: Prof. Zuankai Wang (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Biology and Biomedical Engineering
- Keywords:
- Tissue engineering Biomedical engineering Three-dimensional printing Regenerative medicine
- Resource Type:
- Video
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Video
This channel contains a complete list of physics videos, as well as hundreds of chemistry, astronomy, math, and mechanical engineering videos. The physics videos explain the fundamental concepts of physics with some easy to follow examples on how to solve physics problems. The chemistry videos cover all the basic topics of chemistry, the astronomy videos explain the wonders of Earth and our Universe, and the math videos cover many topics in algebra, trigonometry, pre-calculus, calculus and differential equations.
- Subjects:
- Chemistry, Mathematics and Statistics, Cosmology and Astronomy, Physics, Mechanical Engineering, and Electrical Engineering
- Keywords:
- Chemistry Astronomy Electrical engineering Physics Mathematics Mechanical engineering Kalman filtering
- Resource Type:
- Video
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Video
The lecture commenced with a welcome speech and speaker introduction by Prof. WANG Zuankai, Associate Vice President (Research and Innovation). In his presentation, Prof. Chen first gave a brief introduction to the United Nations’ 17 Sustainable Development Goals (SDGs) as well as the SDG monitoring practices in Mainland China. He pointed out that the Nation has adopted the high quality sustainable development concept, which emphasises harmonising the social, economic and environmental aspects in national development. Next, he elaborated on a pilot project that he led to measure Deqing County’s progress towards SDGs using geospatial and statistical information. The project was selected by the UN Department of Economic and Social Affairs as one of the first 16 good SDGs’ practices in 2020. After that, Prof. Chen shared that the achievement of sustainable development requires holistic and systematic research to build a digital governance system that can provide the basis for the scientific and orderly development of national territorial space. He also explained how territorial space sustainability studies can help unveil and analyse various patterns, such as the distributions of population, enterprises and public service facilities, and the relationships between them. To conclude, Prof. Chen introduced the national program on the development of the Realistic Geospatial Landscape Model (3dRGLm), which can generate digital description and representation of the real 3D geospatial spaces. This new geographic information system can support the Nation in achieving natural resources management and high quality sustainable development.
A question-and-answer session moderated by Prof. DING Xiaoli, Director of the Research Institute for Land and Space (RILS) and Prof. WENG Qihao, Associate Director of RILS, followed. The online and on-site audience engaged in a productive discussion with Prof. Chen.
Even date: 27/03/2024
Speaker: Prof. Jun CHEN (National Geomatics Center of China)
Hosted by: PolyU Academy for Interdisciplinary Research
- Keywords:
- Sustainable development Geospatial data China Sustainable Development Goals Geographic information systems
- Resource Type:
- Video