Richard Yong WANG- Partner, Attorney at Law, Patent Attorney

 

 

 

There are many ways to obtain formulas in scientific research, and there are three main types of formulas that are commonly used in scientific experiments: principle derived formulas, empirical formulas and numerical simulation formulas. Due to the different invention routes and different ways to obtain formulas, it is necessary to choose an appropriate strategy to draft patent applications according to the specific situation of an invention and the way a formula is obtained, so as to facilitate the patent rights acquisition and future enforcement to maximize the protection of achieved technological innovations. Following is an overview of the characteristics of the above three formula types of inventions, with suggestions made on how to draft them.

 

1. Principle Derived Formulas

 

Principle derived formulas are those that are directly derived from scientific principles and mathematical analysis. These formulas, usually derived from basic physical laws, chemical principles, or mathematical theorems through analysis, logical reasoning, and mathematical derivation, have a wide range of application in the fields of science and engineering, such as mechanics, electromagnetism, quantum mechanics, and fluid mechanics.

 

Generally speaking, principle derived formulas usually have the following characteristics: 1) based on fundamental laws as such formulas are usually based on basic scientific laws, like Newton's laws, Maxwell's equations, and thermodynamic laws; 2) offering exact solutions as these formulas are capable of offering exact, rather than approximate or numerical solutions to problems; 3) mathematically derived through mathematical derivation from the basic principles, like differentiation, integration, and algebraic transformation; and 4) experimentally verifiable: the correctness of these formulas can be verified with experimental data, which further enhances the reliability of the theory.

 

Based on the above characteristics, when drafting invention of the type, it is necessary to clearly describe the technical problem or challenge to be addressed, and explain the shortcomings of the prior art in dealing with certain problems. For example, an existing fluid dynamic model cannot accurately predict flow behavior under specific conditions, or an existing chemical reaction model is not accurate enough under high temperature, explaining why new formulas are needed and why existing methods or models cannot effectively solve the problem. This will help highlight the innovativeness and applicability of new formulas.

 

When describing the defects of the prior art, it is usually necessary to provide background information about the prior art or method and point out its limitations. This section requires citations of relevant literature or patents to illustrate that the prior art possibly fails or performs poorly in certain applications or environments.

 

In the description section, describe in detail the underlying scientific principles on which the formula is derived, such as the laws of physics, chemistry, or mathematics. If the invented formula is based on a complex theoretical model, explain its structure. For example, if an invention relating to the electromagnetic field refers to Maxwell's equations, explain how these equations work in the model. In addition, it is often necessary to give preconditions or make assumptions when the formula is derived, such as ignoring air resistance, assuming that the material is homogeneous, etc. These preconditions or assumptions must be stated and explained as to why they are reasonable or necessary. Make sure your definitions are clear and do not use uncommon or vague terms.

 

In the description, the derivation process of a formula should be described in detail. When describing the derivation process of a formula, the derivation process of the formula can be divided into multiple steps, the necessary formula conversion process can be presented, and the step-by-step elaboration is explained, providing mathematical deduction and/or logical reasoning for each step to ensure that each and every step is well founded. For example, how to derive a formula for acceleration from Newton's second law, or a formula for temperature distribution from the equation of heat conduction.

 

In the process of invention, a complex equation often needs to be simplified in order to arrive at a practical formula. For example, suppose that certain variables change very little, or that complex multivariate equations are reduced to a one-dimensional problem. In this case, it is necessary to fully demonstrate that these simplifications are justifiable and that they are explained in the derivation process. If the derivation process involves boundary conditions or initial conditions, these conditions must be clearly described, as they would directly affect the applicability of the formula and the accuracy of the results.

 

It is also important to provide the physical or chemical significance of each variable and parameter in the derived formula, which will help the examiner or the public to understand the function of the formula in practical application. Explaining the meaning of a formula can include, for example, how to describe the working of the system, predict the outcome, or optimize the design to ensure that the formula is not only mathematically correct, but also physically sound. Any theory has certain limitations and the conditions or circumstances to which it applies, so if necessary, it is necessary to state which specific condition or scenario the formula applies to, and the applicable physical conditions, such as the temperature range, pressure range, and material properties. For example, whether the formula is only applicable to materials at high temperature, or whether it can only be used in low velocity flowing fluid. These descriptions help define the scope of protection of the formula.

 

In the embodiment part, the application of a formula is shown by examples. For example, apply the formula to predict the strength of a material under a specific condition, or use it to design a more energy-efficient device. The practical value of the formula is demonstrated with examples, and its accuracy verified with numerical simulation or experimental data, so as to prove the effectiveness of the formula in practical application, and specific data or charts can be provided as support if necessary.

 

When describing the technical effect achieved by an invention, the new formula can be compared with the prior art or method to demonstrate the advantages of the new formula in terms of accuracy, efficiency, or scope of application. This comparative analysis helps demonstrate the innovation and practical value of the new formula. You can visually demonstrate the effect and applicability of the formula by providing relevant charts, say simulated data curves and error analysis charts.

 

Due to the solid theoretical foundation and rigorous derivation process of the principle-derived formulas, there is usually no need for too many embodiments in the description, and usually only a representative embodiment can explain how to use the obtained formula. However, in order to fully expand the scope of application of the formula or the scope of protection of the claims, and avoid limiting the scope of application too narrowly, the inventor should try to demonstrate the applicability of the formula under various conditions, scopes or circumstances, so as to enhance the wide scope of patent protection.

 

2. Empirical formulas

 

An empirical formula is a mathematical expression based on experimental data, observation or experience, with a mathematical relationship obtained by fitting data from experimental measurements, and is used to describe the relationship between two or more variables, but it is not necessarily possible to deduce from basic physical principles.

 

Empirical formulas usually have the following characteristics: 1) based on experimental data, as they are obtained by collecting and analyzing experimental data, which reflects the statistical laws of the data; 2) limited in scope of application, as the formulas obtained are only valid under certain conditions or scopes, beyond which they would no longer be applicable; 3) lacking theoretical explanations, as empirical formulas would not provide in-depth theoretical explanations, but they can describe phenomena; and 4) adjusting parameter as the formulas would contain some empirical parameters, which need to be determined by fitting experimental data.

 

Because an empirical formula requires collection and analysis of a large amount of experimental data to reflect the statistical laws of the data, the description and embodiments are drafted in a way different from that of the principle derived formulas.

 

First of all, the experiment process should be described in detail, explaining the purpose, conditions, equipment, materials, etc. of the experiment, and ensuring that the description of the experimental conditions is detailed enough so that people of ordinary skill in the art can reproduce the experiments. For example, describe the experimental conditions under which the experiment was performed (e.g., temperature, pressure, etc.), which measuring instruments were used, and what the accuracy of the measurement was. To record the data obtained in the experiment in detail, list all the variables and parameters measured in the experiment and determine the role these variables and parameters will play in the final formulas. It is necessary for the measurement method and precision of each variable to be explained to ensure the credibility of the data. If necessary, explain where the data came from and how it was collected, for example, whether the data was derived from one’s own experiment, whether it was combined with third-party data, or whether the data had been verified with multiple experiments. Ensure that the data is reliable, broad and representative.

 

When recording the large amount of relevant data collected through experiments or observations in the description, it is necessary to ensure the diversity and representativeness of the data, and if necessary, describe how the experimental data will be processed and sort out, such as how to remove noise, normalize the data, smooth the data, etc., eliminate outliers and erroneous data, and whether necessary data transformation and normalization are required. The data processing must be rational and in accordance with the scientific method to ensure that the subsequently derived formulas are based on accurate data.

 

When showing how to derive a formula from the obtained experimental data, present the data fitting methods used, such as statistical analysis methods, such as regression analysis, principal component analysis, machine learning, etc., and explain how these methods are applied to data analysis. For example, describe how to arrive at a best-fit formula through multiple linear regressions or identify patterns in data through cluster analysis.

 

In describing the process of deriving a formula from experimental data, you can explain step-by-step how to conclude the relationships between the data through data fitting, regression analysis, or machine learning models. Make sure each step is logical and clear, and has adequate mathematical backing. For example, deriving a polynomial formula from multiple linear regressions, or using neural networks to summarize complex nonlinear relationships. Explain how each variable and parameter in the formula is extracted and defined from the data, explain the relationship between these variables and the experimental data, and why these variables are necessary in the formula. When presenting the summarized formula in standard mathematical form, the physical or chemical meaning of each variable and parameter also needs to be clarified, and its specific meaning be explained to ensure that the formula is concise, clear, and useful directly in different application scenarios.

 

To appropriately extend the scope of protection for an invention relating to such a formula, it is also necessary to make a specific analysis of the formula obtained, to analyze the impact of changes in model parameters or combinations of changes on the prediction results, and to determine key and non-critical parameters. It should be noted that empirical formulas perform well in some cases, and not as well as they should in others, so it is necessary to evaluate the applicability of the empirical formula under different conditions and environments, clarify what condition or scenario the formula is suitable for, such as temperature, pressure, material type, etc., and give the range of situations or parameters to which it is applicable as much as possible, so as to help define the scope of application of the formula and ensure its universality and effectiveness.

 

To prove the validity of an empirical formula obtained, it is also necessary to disclose in the description how the formula could be verified with further experiments. New experiments can be designed, or formulas can be applied to different datasets or experimental conditions to demonstrate how the formulas perform in these situations. For example, verify the predictive power of a formula for different materials or under different operating conditions. Compare the new formula with the existing one or model to demonstrate the advantages of the new formula in terms of accuracy, applicability, or computational efficiency. The key experimental data and their analysis results can be displayed through comparison of experimental data or calculation results. The data should be capable of supporting the derivation process of the formula and demonstrate its validity. For example, provide raw data tables for fitting formulas, regression analysis results, error analysis, etc., to ensure that the experimental data used is broad enough to be representative of the phenomenon that the formula is intended to describe. Insufficient coverage of the data may limit the scope of application of the formula and affect the chances of patentability of an application.

 

A formula should be generalizable enough to avoid over fitting, i.e., it is only applicable to specific datasets and not be generalized to other scenarios. Ensuring that examiners or the public have sufficient grounds to believe that the formula will perform well under a variety of conditions is an important factor in the grant and enforcement of such patents.

 

Anyway, when drafting a patent application relating to a formula based on a large amount of experimental data, it is necessary to describe the experimental design, data processing, formula derivation, and verification process in a comprehensive and detailed manner. By providing clear logical reasoning, data support and practical application examples, as well as verification, the persuasiveness of the patent application and the scope of protection would possibly be expanded, ensuring that the claims cover the core innovation point of the formula, so as to enhance the broad protection and commercial value of the patent.

 

3. Numerical Simulation Formulas

 

A numerical simulation formula refers to one that uses mathematical models to approximate or simulate actual physical phenomena in the fields of scientific computing and engineering. These formulas are not analytic solutions derived directly from the laws of physics, but approximate solutions obtained by numerical methods. They use discretization and approximation to deal with problems that are difficult to solve with analytical methods, allowing for large-scale computation and simulation on the computer.

 

Numerical simulation is an iterative and multi-stage process that requires multiple adjustments and optimizations to obtain accurate results, the accuracy of which is affected by factors, such as the numerical method chosen, the discretization accuracy, the efficiency of the algorithm, and the computer hardware. In numerical simulation, it is critical to ensure the accuracy and stability of the model. Therefore, when performing numerical simulation, the following issues should be noted: 1) the appropriate numerical method should be selected according to the special characteristics of the problem (such as elliptical, parabolic or hyperbolic shape); 2) ensure that the discretization scheme can maintain the physical properties of the original problem, such as conservation laws and symmetry; 3) by simulating under different grid sizes, the convergence and grid independence of the results are checked; 4) for the time-dependent problem, choose the appropriate time step size to ensure stability, and avoid the computational efficiency problem caused by too small step size; 5) the correct application of physically plausible boundary conditions and initial conditions, which directly impact the simulation results; 6) estimate numerical errors (truncation errors and rounding errors) and take measures to control the errors within acceptable limits; and 7) the posterior error estimation method is used to evaluate and improve the accuracy of the numerical solution.

 

Numerical analogue formulas are typically used to simulate complex physical, chemical, biological, or engineering systems, and possibly involve computer programs, algorithms, or specific numerical methods.

 

First, describe in detail the physical phenomenon or engineering problem to be simulated in the application, for example, simulate fluid flow, heat conduction, chemical reactions, or other complex phenomena, explain why numerical simulation is the best way to solve the problem, and describe in detail the underlying mathematical model. If the model involves multiple physical phenomena, determine the physical quantities to be solved and the corresponding boundary conditions. When establishing basic equations that describe a problem based on the laws of physics, the necessary assumptions are often introduced to simplify the problem.

 

When describing in detail the numerical methods used to solve a mathematical model, choose the appropriate numerical method based on the characteristics of the problem, such as the finite element method, the finite difference method, the finite volume method, or the Monte Carlo simulation. If the formula involves a discretization process (for example, converting a continuous equation to a discrete form), describe the steps and methods of discretization. This could include things like mesh generation, time step selection, and space step selection. If there is a relevant calculation program or algorithm for the implementation of numerical simulations, the logic and steps of the program should be described in detail in the description. If a specific software implementation or code is involved, it is preferable to provide pseudo-code or flowcharts, so that the examiner can understand the implementation process of the algorithm. Describe the boundary conditions and initial conditions used in numerical simulations, which directly impact the simulation results, and must be clearly stated.

 

For an invention of numerical simulation formula, the verification of the numerical simulation result accuracy is an important step. By analyzing the results of the numerical simulations, check whether they are reasonable and conform to physical phenomena; When verifying numerical simulation results, provide the results of numerical simulations, including graphs, data, and comparative analysis, explain how these results verify the validity of the numerical model, and compare the numerical simulation results with experimental data, theoretical predictions, or results of the existing simulation methods to prove the superiority of the new formula or method. Verifying the accuracy of numerical simulation is a complex process, and there are already many methods for verification in engineering, and in practical applications, it possibly needs to select one or more appropriate verification methods according to the specific problem and available resources.

 

In the embodiment part, the practical application scenarios of a numerical simulation formula should be described in detail, explaining how the numerical simulation formula is applied in practice. For example, the formula may be used to design more efficient turbine blades, predict the rate of chemical reactions, optimize the thermal management system of buildings, etc., and discuss the potential applications of the numerical simulation formula in different industrial fields, such as aerospace, automotive, chemical engineering, materials science, etc., and these examples can include detailed steps of simulation, parameters used, and ways to interpret the results. This would help expand the scope of patent protection.

 

Relevant drawings can also be given in the patent application, such as flow diagrams of the simulation process, schematic diagrams of the calculation grid, or diagrams of the numerical simulation results. These graphics would help the examiner better understand what the invention is all about.

 

In summary, when drafting a patent application relating to a numerical simulation formula, it is necessary to describe in detail the mathematical model, numerical method, calculation program and practical application scenario. Provide sufficient supporting evidence and examples to demonstrate the effectiveness of the formula in solving a particular problem; and improve the success rate of patent applications by helping the examiner understand the complex numerical simulation process with clear descriptions and diagrams.

 

4. Conclusion

 

As can be seen from the above, when drafting a patent application involving the three types of formulas, it is necessary to make differentiated treatment for the source, derivation process and verification method of the formulas. The principle derived formulas focus on theoretical derivation and a small amount of experimental verification, the experimental summary formulas relies on a large amount of data analysis and extensive application verification, while the numerical simulation formulas need to describe the simulation process and results in detail. Therefore, patent attorneys should pay attention to the different requirements and characteristics of application documents when drafting them, so as to ensure the integrity of patent application documents and improve the legal protection of the patent rights.

 

Following is a brief comparison of the characteristics of patent applications with the three types of formulas in the table below for practitioners' reference.

 

	Principle derived formulas	Experimental summary formulas	Numerical simulation formulas
Formula origin	Based on known scientific principles or theories, the formulas are derived through mathematical derivation, and have a relatively solid theoretical foundation.	Based on a large amount of experimental data, empirical formulas obtained through data analysis and fitting are summaries of complex phenomena and possibly do not have a clear theoretical basis.	Formulas or models, obtained through numerical simulation are usually used for   simulation and prediction of complex systems.
Innovation point	How to derive a new formula from a basic principle, or how to apply an existing principle to a new field.	How to design experiments, collect data, and derive a formula from data analysis. A detailed description of the data source, the method of analysis, and the scope and accuracy of the formula is required.	It's about the simulation method, the modeling process, and how the simulation can be used to derive the formula. It is necessary to describe in detail the boundary conditions, initial conditions, meshing and other technical details of the numerical simulation.
Role of experimental data	Experimental data are often used to verify the   correctness of a formula, not to derive the formula itself. The experimental part can be brief, but should clearly show the actual effect of the formula.	Experimental data are the basis of the formulas, and the experimental design, data collection, and data analysis process should be described in detail. The quality, quantity, and diversity of the data directly determine the reliability of the formulas.	The results of the numerical simulation are equivalent to "experimental data", and the process and results of the simulation should be described in detail. Each step in the simulation, such as meshing and boundary condition settings should be explained.
Data quantity requirement	Only a small amount of experimental data is required to demonstrate the effectiveness and accuracy of the formula in the application.	A large amount of data needs to be provided to show how the formula is derived from data analysis and prove the generalizability and reliability of the formula.	Graphs and data of the simulation results should be provided, and the accuracy and applicability of the simulation verified by comparing it with the actual situation or other models.
Formula formation process	The derivation process of the formula is the core of the invention and must be described in detail. It is necessary to demonstrate every step of the derivation process, from the basic principle to the final formula, to ensure logical rigor.	The derivation process mainly focuses on data analysis methods, such as regression analysis, fitting curves and statistical methods. It is necessary to describe how the formula was derived from the experimental data, as well as the scientific basis for the method used.	Numerical simulation methods are described, detailing each step in the simulation, including meshing, boundary condition setting, and solver selection.
Formula description methods	Detail the mathematical methods used in the derivation, and explain the physical or chemical significance of each step.	Emphasize the empirical nature of the formula, explain which ranges the formula applies to, and explain why the experimental data in the range can support the derivation of the formula.	Demonstrate the simulation results, and explain the accuracy and applicability of the formula by comparing it with actual data, error analysis, etc.
Formula verification methods	The correctness of the formula is usually verified by a small number of experiments, but it can also be verified by comparison with known theories.	It is necessary to verify the universality of the formula through experiments under different conditions, say, under different material, environmental, and process conditions.	The accuracy of the formula is verified by further numerical simulation or practical application. Simulation results in multiple scenarios are needed to prove the reliability of the formula.
Formula application scope	Describe the application of the formula in a particular field and explain its advantages over existing methods.	Demonstrate the effectiveness of the formula in multiple fields or application scenarios, and prove its wide applicability.	Demonstrate the effect of the formula in real-world engineering or industrial applications, and illustrate its application value with concrete examples.

 

 

Author:

 

Mr. Richard Yong Wang

 

Mr. Wang received his bachelor's degree in 1991 from the department of computer science of East China Normal University and his master's degree from the Institute of Computing Technology of the Chinese Academy of Sciences in 1994. In 2005, he received degree of master of laws from Renmin University of China. From 1994 to 2006, Mr. Wang worked with China Patent Agent (HK) Ltd, as a patent attorney and director of Electrical and Electronic Department. Mr. Wang joined Panawell in January 2007.

 

Mr. Wang is a member of the All-China Patent Attorneys Association (ACPAA), Sub-Committee of Electronic and Information Technology of ACPAA, LES China and AIPPI China, and FICPI China.

 

In the past years, Mr. Wang has handled thousands of patent applications for both domestic and foreign clients, and he has extensive experiences in application drafting, responding to office actions, patent reexamination and invalidation proceeding, patent administrative litigation, infringement litigation, software registration and integrated circuit layout design registration. As a very experienced patent attorney and attorney-at-law, Mr. Wang also participated in many patent litigation cases on behalf of a number of multinational companies as leading attorney. Mr. Wang's practices include computer hardware, computer software, communication technology, semiconductor devices and manufacturing process, automatic control, household electrical appliances, and etc.